Lah numbers: Difference between revisions
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12 0 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1
Maximum value from the L(100, *) row: 44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000</pre>
=={{header|Tcl}}==
<lang Tcl>proc prod {from to} {
set r 1
if {$from <= $to} {
set r $from
while {[incr from] <= $to} {
set r [expr {$r * $from}]
}
}
return $r
}
proc US3 {n k} {
if {$n < 0 || $k < 0} {
error "US3(): negative arg ($n,$k)"
}
## L(0,0) = 1
## L(n,0) = 0 if 0 < n
## L(0,k) = 0 if 0 < k
## L(n,k) = 0 if n < k
## L(n,n) = 1
if {$n == $k} {
return 1
}
if {$n == 0 || $k == 0} {
return 0
}
if {$n < $k} {
return 0
}
set nk [list $n $k]
if {[info exists ::US3cache($nk)]} {
return $::US3cache($nk)
}
if {$k == 1} {
## L(n,1) = n!
set r [prod 2 $n]
} else {
## k > 1
## L(n,k) = L(n,k-1) * (n - (k-1)) / ((k-1)*k)
set k1 [expr {$k - 1}]
set r [expr {([US3 $n $k1] * ($n - $k1)) / ($k * $k1)}]
}
set ::US3cache($nk) $r
}
proc main {} {
puts "Unsigned Lah numbers L(n,k):"
set max 12 ;# last n,k to print
set L 10 ;# space to use for 1 number
set minn 1 ;# first row to print
set mink 1 ;# first column to print
puts -nonewline "n\\k"
for {set n $minn} {$n <= $max} {incr n} {
puts -nonewline " [format %${L}d $n]"
}
puts ""
for {set n $minn} {$n <= $max} {incr n} {
puts -nonewline [format %3d $n]
for {set k $mink} {$k <= $n} {incr k} {
puts -nonewline " [format %${L}s [US3 $n $k]]"
}
puts ""
}
set n 100
puts "The maximum value of L($n, k) = "
set maxv 0
set maxk -1
for {set k 0} {$k <= $n} {incr k} {
set v [US3 $n $k]
if {$v > $maxv} {
set maxv $v
set maxk $k
}
}
puts $maxv
puts "([string length $maxv] digits, k=$maxk)"
}
main </lang>
{{out}}
<pre style="font-size:83%">Unsigned Lah numbers L(n,k):
n\k 1 2 3 4 5 6 7 8 9 10 11 12
1 1
2 2 1
3 6 6 1
4 24 36 12 1
5 120 240 120 20 1
6 720 1800 1200 300 30 1
7 5040 15120 12600 4200 630 42 1
8 40320 141120 141120 58800 11760 1176 56 1
9 362880 1451520 1693440 846720 211680 28224 2016 72 1
10 3628800 16329600 21772800 12700800 3810240 635040 60480 3240 90 1
11 39916800 199584000 299376000 199584000 69854400 13970880 1663200 118800 4950 110 1
12 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1
The maximum value of L(100, k) =
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000
(164 digits, k=10)
</pre>
=={{header|zkl}}==
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