Multifactorial

The factorial of a number, written as $n!$ , is defined as $n!=n(n-1)(n-2)...(2)(1)$ .

Multifactorials generalize factorials as follows:

In all cases, the terms in the products are positive integers.

If we define the degree of the multifactorial as the difference in successive terms that are multiplied together for a multifactorial (the number of exclamation marks), then the task is twofold:

Write a function that given n and the degree, calculates the multifactorial.
Use the function to generate and display here a table of the first ten members (1 to 10) of the first five degrees of multifactorial.

Note: The wikipedia entry on multifactorials gives a different formula. This task uses the Wolfram mathworld definition.

360 Assembly[edit]

For maximum compatibility, this program uses only the basic instruction set (S/360 1964 POP).

*        Multifactorial            09/05/2016
MULFACR  CSECT
         USING MULFACR,13
SAVEAR   B     STM-SAVEAR(15)
         DC    17F'0'
STM      STM   14,12,12(13) prolog
         ST    13,4(15)     "
         ST    15,8(13)     "
         LR    13,15        " 
         LA    I,1          i=1
LOOPI    C     I,D          do i=1 to deg
         BH    ELOOPI       leave i
         LA    L,W+4          l=@p
         LA    J,1            j=1
LOOPJ    C     J,N            do j=1 to num
         BH    ELOOPJ         leave j
         LA    R,1              r=1
         LCR   S,I              s=-i
         LR    K,J              k=j
LOOPK    C     K,=F'2'          do k=j to 2 by s
         BL    ELOOPK           leave k
         MR    RR,K               r=r*k
         AR    K,S                k=k+s
         B     LOOPK            next k
ELOOPK   CVD   R,Y              pack r
         MVC   X,=XL12'402020202020202020202120' ed mask
         ED    X,Y+2            edit r 
         MVC   0(8,L),X+4       output r
         LA    L,8(L)           l=l+8
         LA    J,1(J)           j=j+1
         B     LOOPJ          next j
ELOOPJ   WTO   MF=(E,W)
         LA    I,1(I)         i=i+1
         B     LOOPI        next i
ELOOPI   L     13,4(0,13)   epilog
         LM    14,12,12(13) "
         XR    15,15        "
         BR    14           "
N        DC    F'10'        number
D        DC    F'5'         degree
W        DC    0F,H'84',H'0',CL80' ' length,zero,text
X        DS    CL12         temp
Y        DS    D            packed PL8
I        EQU   6
J        EQU   7
K        EQU   8
S        EQU   9
RR       EQU   10           even reg of R for MR opcode
R        EQU   11
L        EQU   12
         END   MULFACR

Output:

       1       2       6      24     120     720    5040   40320  362880 3628800
       1       2       3       8      15      48     105     384     945    3840
       1       2       3       4      10      18      28      80     162     280
       1       2       3       4       5      12      21      32      45     120
       1       2       3       4       5       6      14      24      36      50

Ada[edit]

with Ada.Text_IO; use Ada.Text_IO;
procedure Mfact is
 
   function MultiFact (num : Natural; deg : Positive) return Natural is
      Result, N : Integer := num;
   begin
      if N = 0 then return 1; end if;
      loop
         N := N - deg; exit when N <= 0; Result := Result * N;
      end loop; return Result;
   end MultiFact;
 
begin
   for deg in 1..5 loop
      Put("Degree"& Integer'Image(deg) &":");
      for num in 1..10 loop Put(Integer'Image(MultiFact(num,deg))); end loop;
      New_line;
   end loop;
end Mfact;

Output:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

ALGOL 68[edit]

Translation of C.

BEGIN
   INT highest degree = 5;
   INT largest number = 10;
CO Recursive implementation of multifactorial function CO
   PROC multi fact = (INT n, deg) INT :
   (n <= deg | n | n * multi fact(n - deg, deg));
CO Iterative implementation of multifactorial function CO
   PROC multi fact i = (INT n, deg) INT :
   BEGIN
      INT result := n, nn := n;
      WHILE (nn >= deg + 1) DO
	 result TIMESAB nn - deg;
	 nn MINUSAB deg
      OD;
      result
   END;
CO Print out multifactorials CO
   FOR i TO highest degree DO
      printf (($l, "Degree ", g(0), ":"$, i));
      FOR j TO largest number DO
	 printf (($xg(0)$, multi fact (j, i)))
      OD
   OD
END

Output:


Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

ALGOL W[edit]

Iterative multifactorial based on Ada, AutoHotkey, etc.

begin
    % returns the multifactorial of n with the specified degree %
    integer procedure multifactorial ( integer value n, degree ) ;
        begin
            integer mf, v;
            mf := v := n;
            while begin
                      v := v - degree;
                      v > 1
            end do mf := mf * v;
            mf
        end multifactorial ;
 
    % tests as per task %
    for degree := 1 until 5 do begin
        i_w := 1; s_w := 0; % output formatting %
        write( "Degree: ", degree, ":" );
        for v := 1 until 10 do begin
            writeon( " ", multifactorial( v, degree ) )
        end for_v
    end for_degree
end.

Output:

Degree: 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree: 2: 1 2 3 8 15 48 105 384 945 3840
Degree: 3: 1 2 3 4 10 18 28 80 162 280
Degree: 4: 1 2 3 4 5 12 21 32 45 120
Degree: 5: 1 2 3 4 5 6 14 24 36 50

ANSI Standard BASIC[edit]

Translation of FreeBASIC.

100 FUNCTION multiFactorial (n, degree)
110    IF  n < 2 THEN 
120       LET multiFactorial = 1
130       EXIT FUNCTION
140    END IF
150    LET result = n
160    FOR i = n - degree TO 2 STEP -degree
170       LET result = result * i
180    NEXT i
190    LET multiFactorial = result
200 END FUNCTION
210
220 FOR degree = 1 TO 5
230    PRINT "Degree"; degree; " => ";
240    FOR n = 1 TO 10
250       PRINT multiFactorial(n, degree); " ";
260    NEXT n
270    PRINT 
280 NEXT degree
290 END

AutoHotkey[edit]

Loop, 5 {
    Output .= "Degree " (i := A_Index) ": "
    Loop, 10
        Output .= MultiFact(A_Index, i) (A_Index = 10 ? "`n" : ", ")
}
MsgBox, % Output
 
MultiFact(n, d) {
    Result := n
    while 1 < n -= d
        Result *= n
    return, Result
}

Output:

Degree 1: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800
Degree 2: 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840
Degree 3: 1, 2, 3, 4, 10, 18, 28, 80, 162, 280
Degree 4: 1, 2, 3, 4, 5, 12, 21, 32, 45, 120
Degree 5: 1, 2, 3, 4, 5, 6, 14, 24, 36, 50

C[edit]

Uses: C Runtime (Components:printf,)

 
/* Include statements and constant definitions */
#include <stdio.h>
#define HIGHEST_DEGREE 5
#define LARGEST_NUMBER 10
 
/* Recursive implementation of multifactorial function */
int multifact(int n, int deg){
   return n <= deg ? n : n * multifact(n - deg, deg);
}
 
/* Iterative implementation of multifactorial function */
int multifact_i(int n, int deg){
   int result = n;
   while (n >= deg + 1){
      result *= (n - deg);
      n -= deg;
   }
   return result;
}
 
/* Test function to print out multifactorials */
int main(void){
   int i, j;
   for (i = 1; i <= HIGHEST_DEGREE; i++){
      printf("\nDegree %d: ", i);
      for (j = 1; j <= LARGEST_NUMBER; j++){
         printf("%d ", multifact(j, i));
      }
   }
}

Output:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

C#[edit]

namespace RosettaCode.Multifactorial
{
    using System;
    using System.Linq;
 
    internal static class Program
    {
        private static void Main()
        {
            Console.WriteLine(string.Join(Environment.NewLine,
                                          Enumerable.Range(1, 5)
                                                    .Select(
                                                        degree =>
                                                        string.Join(" ",
                                                                    Enumerable.Range(1, 10)
                                                                              .Select(
                                                                                  number =>
                                                                                  Multifactorial(number, degree))))));
        }
 
        private static int Multifactorial(int number, int degree)
        {
            if (degree < 1)
            {
                throw new ArgumentOutOfRangeException("degree");
            }
 
            var count = 1 + (number - 1) / degree;
            if (count < 1)
            {
                throw new ArgumentOutOfRangeException("number");
            }
 
            return Enumerable.Range(0, count)
                             .Aggregate(1, (accumulator, index) => accumulator * (number - degree * index));
        }
    }
}

Output:

1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50

C++[edit]

 
#include <algorithm>
#include <iostream>
#include <iterator>
/*Generate multifactorials to 9
 
  Nigel_Galloway
  November 14th., 2012.
*/
int main(void) {
   for (int g = 1; g < 10; g++) {
     int v[11], n=0;
     generate_n(std::ostream_iterator<int>(std::cout, " "), 10, [&]{n++; return v[n]=(g<n)? v[n-g]*n : n;});
     std::cout << std::endl;
   }
   return 0;
}

Output:

1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50
1 2 3 4 5 6 7 16 27 40
1 2 3 4 5 6 7 8 18 30
1 2 3 4 5 6 7 8 9 20
1 2 3 4 5 6 7 8 9 10

Clojure[edit]

(defn !! [m n]
  (->> (iterate #(- % m) n) (take-while pos?) (apply *)))
 
(doseq [m (range 1 6)]
  (prn m (map #(!! m %) (range 1 11))))

Output:

1 (1 2 6 24 120 720 5040 40320 362880 3628800)
2 (1 2 3 8 15 48 105 384 945 3840)
3 (1 2 3 4 10 18 28 80 162 280)
4 (1 2 3 4 5 12 21 32 45 120)
5 (1 2 3 4 5 6 14 24 36 50)

Common Lisp[edit]

 
(defun mfac (n m)
  (reduce #'* (loop for i from n downto 1 by m collect i)))
 
(loop for i from 1 to 10
      do (format t "~2@a: ~{~a~^ ~}~%"
                 i (loop for j from 1 to 10
                         collect (mfac j i))))

Output:

 1: 1 2 6 24 120 720 5040 40320 362880 3628800
 2: 1 2 3 8 15 48 105 384 945 3840
 3: 1 2 3 4 10 18 28 80 162 280
 4: 1 2 3 4 5 12 21 32 45 120
 5: 1 2 3 4 5 6 14 24 36 50
 6: 1 2 3 4 5 6 7 16 27 40
 7: 1 2 3 4 5 6 7 8 18 30
 8: 1 2 3 4 5 6 7 8 9 20
 9: 1 2 3 4 5 6 7 8 9 10
10: 1 2 3 4 5 6 7 8 9 10

D[edit]

import std.stdio, std.algorithm, std.range;
 
T multifactorial(T=long)(in int n, in int m) pure /*nothrow*/ {
    T one = 1;
    return reduce!q{a * b}(one, iota(n, 0, -m));
}
 
void main() {
    foreach (immutable m; 1 .. 11)
        writefln("%2d: %s", m, iota(1, 11)
                               .map!(n => multifactorial(n, m)));
}

Output:

 1: 1 2 6 24 120 720 5040 40320 362880 3628800 
 2: 1 2 3 8 15 48 105 384 945 3840 
 3: 1 2 3 4 10 18 28 80 162 280 
 4: 1 2 3 4 5 12 21 32 45 120 
 5: 1 2 3 4 5 6 14 24 36 50 
 6: 1 2 3 4 5 6 7 16 27 40 
 7: 1 2 3 4 5 6 7 8 18 30 
 8: 1 2 3 4 5 6 7 8 9 20 
 9: 1 2 3 4 5 6 7 8 9 10 
10: 1 2 3 4 5 6 7 8 9 10

Dart[edit]

 
main()
{
  int n=5,d=3;
int z= fact(n,d);
print('$n factorial of degree $d is $z');
for(var j=1;j<=5;j++)
{
  print('first 10 numbers of degree $j :');
  for(var i=1;i<=10;i++)
  {   
    int z=fact(i,j);
 print('$z'); 
}
  print('\n');
}
}
 
int fact(int a,int b)
{
 
  if(a<=b||a==0)
    return a;
  if(a>1)
    return a*fact((a-b),b);
}

Elixir[edit]

Translation of: Erlang

defmodule RC do
  def multifactorial(n,d) do
    Enum.take_every(n..1, d) |> Enum.reduce(1, fn x,p -> x*p end)
  end
end
 
Enum.each(1..5, fn d ->
  multifac = for n <- 1..10, do: RC.multifactorial(n,d)
  IO.puts "Degree #{d}: #{inspect multifac}"
end)

Output:

Degree 1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
Degree 2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
Degree 3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
Degree 4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
Degree 5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]

Erlang[edit]

-module(multifac).   
-compile(export_all).
 
multifac(N,D) ->
    lists:foldl(fun (X,P) -> X * P end, 1, lists:seq(N,1,-D)).
 
main() ->
    Ds = lists:seq(1,5),
    Ns = lists:seq(1,10),   
    lists:foreach(fun (D) ->
                          io:format("Degree ~b: ~p~n",[D, [ multifac(N,D) || N <- Ns]])
                  end, Ds).

Output:

5> multifac:main().
Degree 1: [1,2,6,24,120,720,5040,40320,362880,3628800]
Degree 2: [1,2,3,8,15,48,105,384,945,3840]
Degree 3: [1,2,3,4,10,18,28,80,162,280]
Degree 4: [1,2,3,4,5,12,21,32,45,120]
Degree 5: [1,2,3,4,5,6,14,24,36,50]
ok

ERRE[edit]

 
PROGRAM MULTIFACTORIAL
 
PROCEDURE MULTI_FACT(NUM,DEG->MF)
   RESULT=NUM
   N=NUM
   IF N=0 THEN
      MF=1
      EXIT PROCEDURE
   END IF
   LOOP
      N-=DEG
      EXIT IF N<=0
      RESULT*=N
   END LOOP
   MF=RESULT
END PROCEDURE
 
BEGIN
  PRINT(CHR$(12);)
  FOR DEG=1 TO 10 DO
      PRINT("Degree";DEG;":";)
      FOR NUM=1 TO 10 DO
          MULTI_FACT(NUM,DEG->MF)
          PRINT(MF;)
      END FOR
      PRINT
  END FOR
END PROGRAM

Degree 1 : 1  2  6  24  120  720  5040  40320  362880  3628800
Degree 2 : 1  2  3  8  15  48  105  384  945  3840
Degree 3 : 1  2  3  4  10  18  28  80  162  280
Degree 4 : 1  2  3  4  5  12  21  32  45  120
Degree 5 : 1  2  3  4  5  6  14  24  36  50
Degree 6 : 1  2  3  4  5  6  7  16  27  40
Degree 7 : 1  2  3  4  5  6  7  8  18  30
Degree 8 : 1  2  3  4  5  6  7  8  9  20
Degree 9 : 1  2  3  4  5  6  7  8  9  10
Degree 10 : 1  2  3  4  5  6  7  8  9  10

F#[edit]

let rec mfact d = function
    | n when n <= d   -> n
    | n -> n * mfact d (n-d)
 
[<EntryPoint>]
let main argv =
    let (|UInt|_|) = System.UInt32.TryParse >> function | true, v -> Some v | false, _ -> None
    let (maxDegree, maxN) =
        match argv with
            | [| UInt d; UInt n |] -> (int d, int n)
            | [| UInt d |]         -> (int d, 10)
            | _                    -> (5, 10)
    let showFor d = List.init maxN (fun i -> mfact d (i+1)) |> printfn "%i: %A" d
    ignore (List.init maxDegree (fun i -> showFor (i+1)))
    0

1: [1; 2; 6; 24; 120; 720; 5040; 40320; 362880; 3628800]
2: [1; 2; 3; 8; 15; 48; 105; 384; 945; 3840]
3: [1; 2; 3; 4; 10; 18; 28; 80; 162; 280]
4: [1; 2; 3; 4; 5; 12; 21; 32; 45; 120]
5: [1; 2; 3; 4; 5; 6; 14; 24; 36; 50]

Forth[edit]

: !n negate swap 1 dup rot do i * over +loop nip ;
: test cr 6 1 ?do 11 1 ?do i j !n . loop cr loop ;

Output:

test
1 2 6 24 120 720 5040 40320 362880 3628800
1 2 3 8 15 48 105 384 945 3840
1 2 3 4 10 18 28 80 162 280
1 2 3 4 5 12 21 32 45 120
1 2 3 4 5 6 14 24 36 50
 ok

Fortran[edit]

Works with: Fortran version 95 and later

program test
  implicit none
  integer :: i, j, n
 
  do i = 1, 5
    write(*, "(a, i0, a)", advance = "no") "Degree ", i, ": "
    do j = 1, 10
      n = multifactorial(j, i)
      write(*, "(i0, 1x)", advance = "no") n
    end do
    write(*,*)
  end do
 
contains
 
function multifactorial (range, degree)
  integer :: multifactorial, range, degree
  integer :: k
 
  multifactorial = product((/(k, k=range, 1, -degree)/))
 
end function multifactorial
end program test

Output:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

FreeBASIC[edit]

' FB 1.05.0 Win64
 
Function multiFactorial (n As UInteger, degree As Integer) As UInteger
  If  n < 2 Then Return 1
  Var result = n
  For i As Integer = n - degree To 2 Step -degree
    result *= i
  Next
  Return result
End Function
 
For degree As Integer = 1 To 5
  Print "Degree"; degree; " => ";
  For n As Integer = 1 To 10
    Print multiFactorial(n, degree); " ";
  Next n
  Print 
Next degree
 
Print
Print "Press any key to quit"
Sleep

Output:

Degree 1 => 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2 => 1 2 3 8 15 48 105 384 945 3840
Degree 3 => 1 2 3 4 10 18 28 80 162 280
Degree 4 => 1 2 3 4 5 12 21 32 45 120
Degree 5 => 1 2 3 4 5 6 14 24 36 50

FunL[edit]

def multifactorial( n, d ) = product( n..1 by -d )
 
for d <- 1..5
  println( d, [multifactorial(i, d) | i <- 1..10] ))

Output:

1, [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
2, [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
3, [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
4, [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
5, [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]

GAP[edit]

MultiFactorial := function(n, k)
    local r;
    r := 1;
    while n > 1 do
        r := r*n;
        n := n - k;
    od;
    return r;
end;
 
PrintArray(List([1 .. 10], n -> List([1 .. 5], k -> MultiFactorial(n, k))));
[ [        1,        1,        1,        1,        1 ],
  [        2,        2,        2,        2,        2 ],
  [        6,        3,        3,        3,        3 ],
  [       24,        8,        4,        4,        4 ],
  [      120,       15,       10,        5,        5 ],
  [      720,       48,       18,       12,        6 ],
  [     5040,      105,       28,       21,       14 ],
  [    40320,      384,       80,       32,       24 ],
  [   362880,      945,      162,       45,       36 ],
  [  3628800,     3840,      280,      120,       50 ] ]

Go[edit]

package main
 
import "fmt"
 
func multiFactorial(n, k int) int {
    r := 1
    for ; n > 1; n -= k {
        r *= n
    }
    return r
}
 
func main() {
    for k := 1; k <= 5; k++ {
        fmt.Print("degree ", k, ":")
        for n := 1; n <= 10; n++ {
            fmt.Print(" ", multiFactorial(n, k))
        }
        fmt.Println()
    }
}

Output:

degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
degree 2: 1 2 3 8 15 48 105 384 945 3840
degree 3: 1 2 3 4 10 18 28 80 162 280
degree 4: 1 2 3 4 5 12 21 32 45 120
degree 5: 1 2 3 4 5 6 14 24 36 50

Haskell[edit]

mulfac k = 1:s where s = [1 .. k] ++ zipWith (*) s [k+1..]
 
-- for single n
mulfac1 k n = product [n, n-k .. 1]
 
main = mapM_ (print . take 10 . tail . mulfac) [1..5]

Output:

[1,2,6,24,120,720,5040,40320,362880,3628800]
[1,2,3,8,15,48,105,384,945,3840]
[1,2,3,4,10,18,28,80,162,280]
[1,2,3,4,5,12,21,32,45,120]
[1,2,3,4,5,6,14,24,36,50]

Icon and Unicon[edit]

The following is Unicon specific but can be readily translated into Icon:

procedure main(A)
    l := integer(A[1]) | 10
    every writeRow(n := !l, [: mf(!10,n) :])
end
 
procedure writeRow(n, r)
    writes(right(n,3),": ")
    every writes(right(!r,8)|"\n")
end
 
procedure mf(n, m)
    if n <= 0 then return 1
    return n*mf(n-m, m)
end

Sample run:

->mf 5
  1:        1       2       6      24     120     720    5040   40320  362880 3628800
  2:        1       2       3       8      15      48     105     384     945    3840
  3:        1       2       3       4      10      18      28      80     162     280
  4:        1       2       3       4       5      12      21      32      45     120
  5:        1       2       3       4       5       6      14      24      36      50
->

J[edit]

 
   NB. tacit implementation of the recursive c function
   NB. int multifact(int n,int deg){return n<=deg?n:n*multifact(n-deg,deg);}
 
   multifact=: [`([ * - $: ])@.(<~)  
   (a:,<'       degree'),multifact table >:i.10
┌─────────┬──────────────────────────────────────┐
│         │       degree                         │
├─────────┼──────────────────────────────────────┤
│multifact│      1    2   3   4  5  6  7  8  9 10│
├─────────┼──────────────────────────────────────┤
│ 1       │      1    1   1   1  1  1  1  1  1  1│
│ 2       │      2    2   2   2  2  2  2  2  2  2│
│ 3       │      6    3   3   3  3  3  3  3  3  3│
│ 4       │     24    8   4   4  4  4  4  4  4  4│
│ 5       │    120   15  10   5  5  5  5  5  5  5│
│ 6       │    720   48  18  12  6  6  6  6  6  6│
│ 7       │   5040  105  28  21 14  7  7  7  7  7│
│ 8       │  40320  384  80  32 24 16  8  8  8  8│
│ 9       │ 362880  945 162  45 36 27 18  9  9  9│
│10       │3628800 3840 280 120 50 40 30 20 10 10│
└─────────┴──────────────────────────────────────┘

Java[edit]

public class MultiFact {
	private static long multiFact(long n, int deg){
		long ans = 1;
		for(long i = n; i > 0; i -= deg){
			ans *= i;
		}
		return ans;
	}
 
	public static void main(String[] args){
		for(int deg = 1; deg <= 5; deg++){
			System.out.print("degree " + deg + ":");
			for(long n = 1; n <= 10; n++){
				System.out.print(" " + multiFact(n, deg));
			}
			System.out.println();
		}
	}
}

Output:

degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
degree 2: 1 2 3 8 15 48 105 384 945 3840
degree 3: 1 2 3 4 10 18 28 80 162 280
degree 4: 1 2 3 4 5 12 21 32 45 120
degree 5: 1 2 3 4 5 6 14 24 36 50

JavaScript[edit]

Iterative[edit]

Translation of: C

 
function multifact(n, deg){
	var result = n;
	while (n >= deg + 1){
		result *= (n - deg);
		n -= deg;
	}
	return result;
}

 
function test (n, deg) {
	for (var i = 1; i <= deg; i ++) {
		var results = '';
		for (var j = 1; j <= n; j ++) {
			results += multifact(j, i) + ' ';
		}
		console.log('Degree ' + i + ': ' + results);
	}
}

Output:

 
test(10, 5)
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 
Degree 2: 1 2 3 8 15 48 105 384 945 3840 
Degree 3: 1 2 3 4 10 18 28 80 162 280 
Degree 4: 1 2 3 4 5 12 21 32 45 120 
Degree 5: 1 2 3 4 5 6 14 24 36 50

Recursive[edit]

Translation of: C

function multifact(n, deg){
    return n <= deg ? n : n * multifact(n - deg, deg);
}

Test

function test (n, deg) {
    for (var i = 1; i <= deg; i ++) {
        var results = '';
        for (var j = 1; j <= n; j ++) {
            results += multifact(j, i) + ' ';
        }
        console.log('Degree ' + i + ': ' + results);
    }
}

Output:

 
test(10, 5)
Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 
Degree 2: 1 2 3 8 15 48 105 384 945 3840 
Degree 3: 1 2 3 4 10 18 28 80 162 280 
Degree 4: 1 2 3 4 5 12 21 32 45 120 
Degree 5: 1 2 3 4 5 6 14 24 36 50

jq[edit]

Works with: jq version 1.4

# Input: n
# Output: n * (n - d) * (n - 2d) ...
def multifactorial(d):
  . as $n
  | ($n / d | floor) as $k
  | reduce ($n - (d * range(0; $k))) as $i (1; . * $i);

# Print out a d-by-n table of multifactorials neatly:
def table(d; n):
  def lpad(i): tostring | (i - length) * " " + .;
  def pp(stream): reduce stream as $i (""; . + ($i | lpad(8)));
 
  range(1; d+1) as $d | "Degree \($d): \( pp(range(1; n+1) | multifactorial($d)) )";

The specific task:

table(5; 10)

Output:

$ jq -n -r -f Multifactorial.jq
Degree 1:        1       2       6      24     120     720    5040   40320  362880 3628800
Degree 2:        1       2       3       8      15      48     105     384     945    3840
Degree 3:        1       1       3       4       5      18      28      40     162     280
Degree 4:        1       1       1       4       5       6       7      32      45      60
Degree 5:        1       1       1       1       5       6       7       8       9      50

Julia[edit]

multifact calculates the mulitfactorial function iteratively.

 
function multifact{T<:Integer,U<:Integer}(n::T, k::U)
    -1<n && 0<k || throw(DomainError())
    1 < k || return factorial(n)
    r = one(T)
    for i in n:-k:2
        r *= i
    end
    return r
end
 
khi = 5
nhi = 10
println("Showing multifactorial for n in [1,", nhi, "] and k in [1,", khi, "].")
for k = 1:khi
    a = Int64[multifact(i, k) for i in 1:nhi]
    lab = "n"*"!"^k
    println(@sprintf("  %-6s =>  ", lab), a)
end

Output:

Showing multifactorial for n in [1,10] and k in [1,5].
  n!     =>  [1,2,6,24,120,720,5040,40320,362880,3628800]
  n!!    =>  [1,2,3,8,15,48,105,384,945,3840]
  n!!!   =>  [1,2,3,4,10,18,28,80,162,280]
  n!!!!  =>  [1,2,3,4,5,12,21,32,45,120]
  n!!!!! =>  [1,2,3,4,5,6,14,24,36,50]

Kotlin[edit]

fun multifactorial(n: Long, d: Int) : Long {
    val r = n % d
    return (1..n).filter { it % d == r } .reduce { i, p -> i * p }
}
 
fun main(args: Array<String>) {
    val m = 5
    val r = 1..10L
    for (d in 1..m) {
        print("%${m}s:".format( "!".repeat(d)))
        r.forEach { print(" " + multifactorial(it, d)) }
        println()
    }
}

Output:

    !: 1 2 6 24 120 720 5040 40320 362880 3628800
   !!: 1 2 3 8 15 48 105 384 945 3840
  !!!: 1 2 3 4 10 18 28 80 162 280
 !!!!: 1 2 3 4 5 12 21 32 45 120
!!!!!: 1 2 3 4 5 6 14 24 36 50

Lua[edit]

function multiFact (n, degree)
    local fact = 1
    for i = n, 2, -degree do
        fact = fact * i
    end
    return fact
end
 
print("Degree\t|\tMultifactorials 1 to 10")
print(string.rep("-", 52))
for d = 1, 5 do
    io.write(" " .. d, "\t| ")
    for n = 1, 10 do
        io.write(multiFact(n, d) .. " ")
    end
    print()
end

Output:

Degree  |       Multifactorials 1 to 10
----------------------------------------------------
 1      | 1 2 6 24 120 720 5040 40320 362880 3628800
 2      | 1 2 3 8 15 48 105 384 945 3840
 3      | 1 2 3 4 10 18 28 80 162 280
 4      | 1 2 3 4 5 12 21 32 45 120
 5      | 1 2 3 4 5 6 14 24 36 50

Mathematica[edit]

Multifactorial[n_, m_] := Abs[ Apply[ Times, Range[-n, -1, m]]]
Table[ Multifactorial[j, i], {i, 5}, {j, 10}] // TableForm

Output:

1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50

МК-61/52[edit]

П1	<->	П0	П2	ИП0	ИП1	1	+	-	x>=0
23	ИП2	ИП0	ИП1	-	*	П2	ИП0	ИП1	-
П1	БП	04	ИП2	С/П

Instruction: number ^ degree В/О С/П

Nim[edit]

# Recursive
proc multifact(n, deg): int =
  result = (if n <= deg: n else: n * multifact(n - deg, deg))
 
# Iterative
proc multifactI(n, deg): int =
  result = n
  var n = n
  while n >= deg + 1:
    result *= n - deg
    n -= deg
 
for i in 1..5:
  stdout.write "\nDegree ", i, ": "
  for j in 1..10:
    stdout.write multifactI(j, i), " "

Output:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 
Degree 2: 1 2 3 8 15 48 105 384 945 3840 
Degree 3: 1 2 3 4 10 18 28 80 162 280 
Degree 4: 1 2 3 4 5 12 21 32 45 120 
Degree 5: 1 2 3 4 5 6 14 24 36 50

Objeck[edit]

Translation of: C

 
class Multifact {
   function : MultiFact(n : Int, deg : Int) ~ Int {
      result := n;
      while (n >= deg + 1){
         result *= (n - deg);
         n -= deg;
      };
 
      return result;
   }
 
   function : Main(args : String[]) ~ Nil {
      for (i := 1; i <= 5; i+=1;){
         IO.Console->Print("Degree ")->Print(i)->Print(": ");
         for (j := 1; j <= 10; j+=1;){
            IO.Console->Print(' ')->Print(MultiFact(j, i));
         };
         IO.Console->PrintLine();
      };
   }
}

Output:

Degree 1:  1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2:  1 2 3 8 15 48 105 384 945 3840
Degree 3:  1 2 3 4 10 18 28 80 162 280
Degree 4:  1 2 3 4 5 12 21 32 45 120
Degree 5:  1 2 3 4 5 6 14 24 36 50

Oforth[edit]

: multifact(n, deg)  1 while( n 0 > ) [ n * n deg - ->n ] ;
 
: printMulti
| i |
   5 loop: i [ System.Out i << " : " << 10 seq map(#[ i multifact]) << cr ] ;

Output:

1 : [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
2 : [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
3 : [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
4 : [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
5 : [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]

PARI/GP[edit]

fac(n,d)=prod(k=0,(n-1)\d,n-k*d)
for(k=1,5,for(n=1,10,print1(fac(n,k)" "));print)

1 2 6 24 120 720 5040 40320 362880 3628800 
1 2 3 8 15 48 105 384 945 3840 
1 2 3 4 10 18 28 80 162 280 
1 2 3 4 5 12 21 32 45 120 
1 2 3 4 5 6 14 24 36 50

Perl[edit]

{ # <-- scoping the cache and bigint clause
	my @cache;
	use bigint;
	sub mfact {
		my ($s, $n) = @_;
		return 1 if $n <= 0;
		$cache[$s][$n] //= $n * mfact($s, $n - $s);
	}
}
 
for my $s (1 .. 10) {
	print "step=$s: ";
	print join(" ", map(mfact($s, $_), 1 .. 10)), "\n";
}

Output:

step=1: 1 2 6 24 120 720 5040 40320 362880 3628800
step=2: 1 2 3 8 15 48 105 384 945 3840
step=3: 1 2 3 4 10 18 28 80 162 280
step=4: 1 2 3 4 5 12 21 32 45 120
step=5: 1 2 3 4 5 6 14 24 36 50
step=6: 1 2 3 4 5 6 7 16 27 40
step=7: 1 2 3 4 5 6 7 8 18 30
step=8: 1 2 3 4 5 6 7 8 9 20
step=9: 1 2 3 4 5 6 7 8 9 10
step=10: 1 2 3 4 5 6 7 8 9 10

We can also do this iteratively. ntheory's vecprod makes bigint products if needed, so we don't have to worry about it.

Library: ntheory

use ntheory qw/vecprod/;
 
sub mfac {
  my($n,$d) = @_;
  vecprod(map { $n - $_*$d } 0 .. int(($n-1)/$d));
}
 
for my $degree (1..5) {
  say "$degree: ",join(" ",map{mfac($_,$degree)} 1..10);
}

Output:

1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50

Perl 6[edit]

for 1 .. 5 -> $degree {
    sub mfact($n) { [*] $n, *-$degree ...^ * <= 0 };
    say "$degree: ", map &mfact, 1..10
}

Output:

1: 1 2 6 24 120 720 5040 40320 362880 3628800
2: 1 2 3 8 15 48 105 384 945 3840
3: 1 2 3 4 10 18 28 80 162 280
4: 1 2 3 4 5 12 21 32 45 120
5: 1 2 3 4 5 6 14 24 36 50

Phix[edit]

function multifactorial(integer n, integer order)
atom res = 1
    if n>0 then
        res = n*multifactorial(n-order,order)
    end if 
    return res
end function
 
sequence s = repeat(0,10)
for i=1 to 5 do
    for j=1 to 10 do
        s[j] = multifactorial(j,i)
    end for
    ?s
end for

Output:

{1,2,6,24,120,720,5040,40320,362880,3628800}
{1,2,3,8,15,48,105,384,945,3840}
{1,2,3,4,10,18,28,80,162,280}
{1,2,3,4,5,12,21,32,45,120}
{1,2,3,4,5,6,14,24,36,50}

PicoLisp[edit]

Translation of: C

(de multifact (N Deg)
   (let Res N
      (while (> N Deg)
         (setq Res (* Res (dec 'N Deg))) )
      Res ) )
 
(for I 5
   (prin "Degree " I ":")
   (for J 10
      (prin " " (multifact J I)) )
   (prinl) )

Output:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

PL/I[edit]

 
multi: procedure options (main);      /* 29 October 2013 */
   declare (i, j, n) fixed binary;
   declare text character (6) static initial ('n!!!!!');
 
   do i = 1 to 5;
      put skip edit (substr(text, 1, i+1), '=' ) (A, COLUMN(8));
      do n = 1 to 10;
         put edit ( trim( multifactorial(n,i) ) ) (X(1), A);
      end;
   end;
 
multifactorial: procedure (n, j) returns (fixed(15));
   declare (n, j) fixed binary;
   declare f fixed (15), m fixed(15);
 
      f, m = n;
      do while (m > j); f = f * (m-fixed(j)); m = m - j; end;
      return (f);
end multifactorial;
 
end multi;

Output:

n!     = 1 2 6 24 120 720 5040 40320 362880 3628800
n!!    = 1 2 3 8 15 48 105 384 945 3840
n!!!   = 1 2 3 4 10 18 28 80 162 280
n!!!!  = 1 2 3 4 5 12 21 32 45 120
n!!!!! = 1 2 3 4 5 6 14 24 36 50

Plain $T e X$ [edit]

Works with an etex engine.

\long\def\antefi#1#2\fi{#2\fi#1}
\def\fornum#1=#2to#3(#4){%
	\edef#1{\number\numexpr#2}\edef\fornumtemp{\noexpand\fornumi\expandafter\noexpand\csname fornum\string#1\endcsname
		{\number\numexpr#3}{\ifnum\numexpr#4<0 <\else>\fi}{\number\numexpr#4}\noexpand#1}\fornumtemp
}
\long\def\fornumi#1#2#3#4#5#6{\def#1{\unless\ifnum#5#3#2\relax\antefi{#6\edef#5{\number\numexpr#5+(#4)\relax}#1}\fi}#1}
\newcount\result
\def\multifact#1#2{%
	\result=1
	\fornum\multifactiter=#1 to 1(-#2){\multiply\result\multifactiter}%
	\number\result
}
\fornum\degree=1 to 5(+1){Degree \degree: \fornum\ii=1 to 10(+1){\multifact\ii\degree\space\space}\par}
\bye

Output pdf looks like:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

Python[edit]

Python: Iterative[edit]

>>> from functools import reduce
>>> from operator import mul
>>> def mfac(n, m): return reduce(mul, range(n, 0, -m))
 
>>> for m in range(1, 11): print("%2i: %r" % (m, [mfac(n, m) for n in range(1, 11)]))
 
 1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
 2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
 3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
 4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
 5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
 6: [1, 2, 3, 4, 5, 6, 7, 16, 27, 40]
 7: [1, 2, 3, 4, 5, 6, 7, 8, 18, 30]
 8: [1, 2, 3, 4, 5, 6, 7, 8, 9, 20]
 9: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
10: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
>>>

Python: Recursive[edit]

>>> def mfac2(n, m): return n if n <= (m + 1) else n * mfac2(n - m, m)
 
>>> for m in range(1, 6): print("%2i: %r" % (m, [mfac2(n, m) for n in range(1, 11)]))
 
 1: [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
 2: [1, 2, 3, 8, 15, 48, 105, 384, 945, 3840]
 3: [1, 2, 3, 4, 10, 18, 28, 80, 162, 280]
 4: [1, 2, 3, 4, 5, 12, 21, 32, 45, 120]
 5: [1, 2, 3, 4, 5, 6, 14, 24, 36, 50]
>>>

R[edit]

 
#x is Input
#n is Factorial Number
multifactorial=function(x,n){
  if(x<=n+1){
    return(x)
  }else{
    return(x*multifactorial(x-n,n))
  }
}

Racket[edit]

#lang racket
 
(define (multi-factorial-fn m)
  (lambda (n)
    (let inner ((acc 1) (n n))
      (if (<= n m) (* acc n)
          (inner (* acc n) (- n m))))))
 
;; using (multi-factorial-fn m) as a first-class function
(for*/list ([m (in-range 1 (add1 5))] [mf-m (in-value (multi-factorial-fn m))])
  (for/list ([n (in-range 1 (add1 10))])
  (mf-m n)))
 
(define (multi-factorial m n) ((multi-factorial-fn m) n))
 
(for/list ([m (in-range 1 (add1 5))])
  (for/list ([n (in-range 1 (add1 10))])
  (multi-factorial m n)))

Output:

'((1 2 6 24 120 720 5040 40320 362880 3628800)
  (1 2 3 8 15 48 105 384 945 3840)
  (1 2 3 4 10 18 28 80 162 280)
  (1 2 3 4 5 12 21 32 45 120)
  (1 2 3 4 5 6 14 24 36 50))
'((1 2 6 24 120 720 5040 40320 362880 3628800)
  (1 2 3 8 15 48 105 384 945 3840)
  (1 2 3 4 10 18 28 80 162 280)
  (1 2 3 4 5 12 21 32 45 120)
  (1 2 3 4 5 6 14 24 36 50))

REXX[edit]

This version also handles zero as well as positive integers.

/*REXX program calculates and displays K-fact (multifactorial) of non-negative integers.*/
numeric digits 1000                              /*get ka-razy with the decimal digits. */
parse arg num deg .                              /*get optional arguments from the C.L. */
if num=='' | num==","   then num=15              /*Not specified?  Then use the default.*/
if deg=='' | deg==","   then deg=10              /* "      "         "   "   "     "    */
say '═══showing multiple factorials (1 ──►'     deg")  for numbers  1 ──►"      num
say
     do d=1  for deg                             /*the factorializing (degree)  of  !'s.*/
     _=                                          /*the list of factorials  (so far).    */
            do f=1  for num                      /* ◄── perform a ! from  1 ───► number.*/
            _=_  Kfact(f, d)                     /*build a  list  of factorial products.*/
            end   /*f*/                          /* [↑]    D   can default to  unity.   */
 
     say right('n'copies("!", d), 1+deg)    right('['d"]", 2+length(num) )':'     _
     end          /*d*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Kfact: procedure; !=1;   do j=arg(1)  to 2  by -word(arg(2) 1,1);  !=!*j;  end;   return !

output when using the default input:

═══showing multiple factorials (1 ──► 10)  for numbers  1 ──► 15

         n!  [1]:  1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
        n!!  [2]:  1 2 3 8 15 48 105 384 945 3840 10395 46080 135135 645120 2027025
       n!!!  [3]:  1 2 3 4 10 18 28 80 162 280 880 1944 3640 12320 29160
      n!!!!  [4]:  1 2 3 4 5 12 21 32 45 120 231 384 585 1680 3465
     n!!!!!  [5]:  1 2 3 4 5 6 14 24 36 50 66 168 312 504 750
    n!!!!!!  [6]:  1 2 3 4 5 6 7 16 27 40 55 72 91 224 405
   n!!!!!!!  [7]:  1 2 3 4 5 6 7 8 18 30 44 60 78 98 120
  n!!!!!!!!  [8]:  1 2 3 4 5 6 7 8 9 20 33 48 65 84 105
 n!!!!!!!!!  [9]:  1 2 3 4 5 6 7 8 9 10 22 36 52 70 90
n!!!!!!!!!! [10]:  1 2 3 4 5 6 7 8 9 10 11 24 39 56 75

Ring[edit]

 
see "Degree  " +  "|" + "           Multifactorials 1 to 10" + nl
see copy("-", 52) + nl
for d = 1 to 5 
    see "" + d + "       " + "| "
    for n = 1 to 10 
        see "" + multiFact(n, d) + " "
    next
    see nl
next
 
func multiFact n, degree
     fact = 1
     for i = n to 2 step -degree 
         fact = fact * i
     next
     return fact

Output:

Degree  |           Multifactorials 1 to 10
----------------------------------------------------
1       | 1 2 6 24 120 720 5040 40320 362880 3628800
2       | 1 2 3 8 15 48 105 384 945 3840
3       | 1 2 3 4 10 18 28 80 162 280
4       | 1 2 3 4 5 12 21 32 45 120
5       | 1 2 3 4 5 6 14 24 36 50

Ruby[edit]

 
def multifact(n, d)
  n.step(1, -d).inject( :* )
end
 
(1..5).each {|d| puts "Degree #{d}: #{(1..10).map{|n| multifact(n, d)}.join "\t"}"}

output

Degree 1: 1	2	6	24	120	720	5040	40320	362880	3628800
Degree 2: 1	2	3	8	15	48	105	384	945	3840
Degree 3: 1	2	3	4	10	18	28	80	162	280
Degree 4: 1	2	3	4	5	12	21	32	45	120
Degree 5: 1	2	3	4	5	6	14	24	36	50

Run BASIC[edit]

 
print "Degree  " +  "|" + "           Multifactorials 1 to 10" + nl
print copy("-", 52) + nl
for d = 1 to 5 
    print "" + d + "       " + "| "
    for n = 1 to 10 
        print "" + multiFact(n, d) + " ";
    next
    print
next
 
function multiFact(n,degree)
     fact = 1
     for i = n to 2 step -degree 
         fact = fact * i
     next
     multiFact = fact 
 end function

Degree  |           Multifactorials 1 to 10
--------|---------------------------------------------
1       | 1 2 6 24 120 720 5040 40320 362880 3628800 
2       | 1 2 3 8 15 48 105 384 945 3840 
3       | 1 2 3 4 10 18 28 80 162 280 
4       | 1 2 3 4 5 12 21 32 45 120 
5       | 1 2 3 4 5 6 14 24 36 50

Scala[edit]

 
def multiFact(n : BigInt, degree : BigInt) = (n to 1 by -degree).product
 
for{
  degree <- 1 to 5
  str = (1 to 10).map(n => multiFact(n, degree)).mkString(" ")
} println(s"Degree $degree: $str")

Output:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

Scheme[edit]

 
(import (scheme base)
        (scheme write)
        (srfi 1))
 
(define (multi-factorial n m)
  (fold * 1 (iota (ceiling (/ n m)) n (- m))))
 
(for-each 
  (lambda (degree) 
    (display (string-append "degree "
                            (number->string degree)
                            ": "))
    (for-each 
      (lambda (num) 
        (display (string-append (number->string (multi-factorial num degree))
                                " ")))
      (iota 10 1))
    (newline))
  (iota 5 1))

Output:

degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 
degree 2: 1 2 3 8 15 48 105 384 945 3840 
degree 3: 1 2 3 4 10 18 28 80 162 280 
degree 4: 1 2 3 4 5 12 21 32 45 120 
degree 5: 1 2 3 4 5 6 14 24 36 50

Seed7[edit]

$ include "seed7_05.s7i";
 
const func integer: multiFact (in var integer: num, in integer: degree) is func
  result
    var integer: multiFact is 1;
  begin
    while num > 1 do
      multiFact *:= num;
      num -:= degree;
    end while;
  end func;
 
const proc: main is func
  local
    var integer: degree is 0;
    var integer: num is 0;
  begin
    for degree range 1 to 5 do
      write("Degree " <& degree <& ": ");
      for num range 1 to 10 do
        write(multiFact(num, degree) <& " ");
      end for;
      writeln;
    end for;
  end func;

Output:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800 
Degree 2: 1 2 3 8 15 48 105 384 945 3840 
Degree 3: 1 2 3 4 10 18 28 80 162 280 
Degree 4: 1 2 3 4 5 12 21 32 45 120 
Degree 5: 1 2 3 4 5 6 14 24 36 50

Sidef[edit]

func mfact(s, n) {
    n > 0 ? (n * mfact(s, n-s)) : 1
}
 
{ |s|
    say "step=#{s}: #{{|n| mfact(s, n)}.map(1..10).join(' ')}"
} << 1..10

Output:

step=1: 1 2 6 24 120 720 5040 40320 362880 3628800
step=2: 1 2 3 8 15 48 105 384 945 3840
step=3: 1 2 3 4 10 18 28 80 162 280
step=4: 1 2 3 4 5 12 21 32 45 120
step=5: 1 2 3 4 5 6 14 24 36 50
step=6: 1 2 3 4 5 6 7 16 27 40
step=7: 1 2 3 4 5 6 7 8 18 30
step=8: 1 2 3 4 5 6 7 8 9 20
step=9: 1 2 3 4 5 6 7 8 9 10
step=10: 1 2 3 4 5 6 7 8 9 10

Tcl[edit]

Works with: Tcl version 8.6

package require Tcl 8.6
 
proc mfact {n m} {
    set mm [expr {-$m}]
    for {set r $n} {[incr n $mm] > 1} {set r [expr {$r * $n}]} {}
    return $r
}
 
foreach n {1 2 3 4 5 6 7 8 9 10} {
    puts $n:[join [lmap m {1 2 3 4 5 6 7 8 9 10} {mfact $m $n}] ,]
}

Output:

1:1,2,6,24,120,720,5040,40320,362880,3628800
2:1,2,3,8,15,48,105,384,945,3840
3:1,2,3,4,10,18,28,80,162,280
4:1,2,3,4,5,12,21,32,45,120
5:1,2,3,4,5,6,14,24,36,50
6:1,2,3,4,5,6,7,16,27,40
7:1,2,3,4,5,6,7,8,18,30
8:1,2,3,4,5,6,7,8,9,20
9:1,2,3,4,5,6,7,8,9,10
10:1,2,3,4,5,6,7,8,9,10

uBasic/4tH[edit]

Translation of: Run BASIC

print "Degree  |           Multifactorials 1 to 10"
for x = 1 to 53 : print "-"; : next : print
for d = 1 to 5
  print d;"       ";"| ";
  for n = 1 to 10
    print FUNC(_multiFact(n, d));" ";
  next
  print
next
 
end
 
_multiFact param (2)
  local (2)
  c@ = 1
  for d@ = a@ to 2 step -b@
    c@ = c@ * d@
  next
return (c@)

Output:

Degree  |           Multifactorials 1 to 10
-----------------------------------------------------
1       | 1 2 6 24 120 720 5040 40320 362880 3628800
2       | 1 2 3 8 15 48 105 384 945 3840
3       | 1 2 3 4 10 18 28 80 162 280
4       | 1 2 3 4 5 12 21 32 45 120
5       | 1 2 3 4 5 6 14 24 36 50

0 OK, 0:1063

VBScript[edit]

 
Function multifactorial(n,d)
	If n = 0 Then
		multifactorial = 1
	Else
		For i = n To 1 Step -d
			If i = n Then
				multifactorial = n
			Else
				multifactorial = multifactorial * i
			End If
		Next
	End If
End Function
 
For j = 1 To 5
	WScript.StdOut.Write "Degree " & j & ": "
	For k = 1 To 10
		If k = 10 Then
			WScript.StdOut.Write multifactorial(k,j)
		Else
			WScript.StdOut.Write multifactorial(k,j) & " "
		End If
	Next
	WScript.StdOut.WriteLine
Next

Output:

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

Wortel[edit]

@let {
  facd  &[d n]?{<= n d n @prod@range[n 1 @-d]}
  ; tacit implementation
  facdt ^(!?(/^> .1 ^(@prod @range ~1jdtShj &^!(@- @id))) @,)
  ; recursive
  facdrec &[n d] ?{<= n d n *n !!facdrec -n d d}
  ; output
  l @to 10
  ~@each @to 5 &n !console.log "Degree {n}: {@join @s !*\facd n l}"
}

Output

Degree 1: 1 2 6 24 120 720 5040 40320 362880 3628800
Degree 2: 1 2 3 8 15 48 105 384 945 3840
Degree 3: 1 2 3 4 10 18 28 80 162 280
Degree 4: 1 2 3 4 5 12 21 32 45 120
Degree 5: 1 2 3 4 5 6 14 24 36 50

XPL0[edit]

code ChOut=8, CrLf=9, IntOut=11;
 
func MultiFac(N, D);    \Return multifactorial of N in degree D
int  N, D;
int  F;
[F:= 1;
repeat  F:= F*N;
        N:= N-D;
until   N <= 1;
return F;
];
 
int I, J;               \generate table of multifactorials
for J:= 1 to 5 do
    [for I:= 1 to 10 do
        [IntOut(0, MultiFac(I, J));  ChOut(0, 9\tab\)];
    CrLf(0);
    ]

Output:

1       2       6       24      120     720     5040    40320   362880  3628800 
1       2       3       8       15      48      105     384     945     3840    
1       2       3       4       10      18      28      80      162     280     
1       2       3       4       5       12      21      32      45      120     
1       2       3       4       5       6       14      24      36      50

zkl[edit]

fcn mfact(n,m){ [n..1,-m].reduce('*,1) }
foreach m in ([1..5]){ println("%d: %s".fmt(m,[1..10].apply(mfact.fp1(m)))) }

Output:

1: L(1,2,6,24,120,720,5040,40320,362880,3628800)
2: L(1,2,3,8,15,48,105,384,945,3840)
3: L(1,2,3,4,10,18,28,80,162,280)
4: L(1,2,3,4,5,12,21,32,45,120)
5: L(1,2,3,4,5,6,14,24,36,50)

Multifactorial

Contents

360 Assembly[edit]

Ada[edit]

ALGOL 68[edit]

ALGOL W[edit]

ANSI Standard BASIC[edit]

AutoHotkey[edit]

C[edit]

C#[edit]

C++[edit]

Clojure[edit]

Common Lisp[edit]

D[edit]

Dart[edit]

Elixir[edit]

Erlang[edit]

ERRE[edit]

F#[edit]

Forth[edit]

Fortran[edit]

FreeBASIC[edit]

FunL[edit]

GAP[edit]

Go[edit]

Haskell[edit]

Icon and Unicon[edit]

J[edit]

Java[edit]

JavaScript[edit]

Iterative[edit]

Recursive[edit]

jq[edit]

Julia[edit]

Kotlin[edit]

Lua[edit]

Mathematica[edit]

МК-61/52[edit]

Nim[edit]

Objeck[edit]

Oforth[edit]

PARI/GP[edit]

Perl[edit]

Perl 6[edit]

Phix[edit]

PicoLisp[edit]

PL/I[edit]

Plain TeX[edit]

Python[edit]

Python: Iterative[edit]

Python: Recursive[edit]

R[edit]

Racket[edit]

REXX[edit]

Ring[edit]

Ruby[edit]

Run BASIC[edit]

Scala[edit]

Scheme[edit]

Seed7[edit]

Sidef[edit]

Tcl[edit]

uBasic/4tH[edit]

VBScript[edit]

Wortel[edit]

XPL0[edit]

zkl[edit]

Plain $T e X$ [edit]