Lah numbers: Difference between revisions
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</pre>
=={{header|jq}}==
The table can be produced by either jq or gojq (the Go implementation of jq),
but gojq is required to produce the precise maximum value.
<lang jq>## Generic functions
def factorial: reduce range(2;.+1) as $i (1; . * $i);
# nCk assuming n >= k
def binomial($n; $k):
if $k > $n / 2 then binomial($n; $n-$k)
else (reduce range($k+1; $n+1) as $i (1; . * $i)) as $numerator
| reduce range(1;1+$n-$k) as $i ($numerator; . / $i)
end;
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
def max(s): reduce s as $x (-infinite; if $x > . then $x else . end);
def lah($n; $k; $signed):
if $n == $k then 1
elif $n == 0 or $k == 0 or $k > $n then 0
elif $k == 1 then $n|factorial
else
(binomial($n; $k) * binomial($n - 1; $k - 1) * (($n - $k)|factorial)) as $unsignedvalue
| if $signed and ($n % 1 == 1)
then -$unsignedvalue
else $unsignedvalue
end
end;
def lah($n; $k): lah($n;$k;false);
</lang>
'''The task'''
<lang jq>def printlahtable($kmax):
def pad: lpad(12);
reduce range(0;$kmax+1) as $k ("n/k"|lpad(4); . + ($k|pad)),
(range(0; $kmax+1) as $n
| reduce range(0;$n+1) as $k ($n|lpad(4);
. + (lah($n; $k) | pad)) ) ;
def task:
"Unsigned Lah numbers up to n==12",
printlahtable(12), "",
"The maxiumum of lah(100, _) is: \(max( lah(100; range(0;101)) ))"
;
task
</lang>
{{out}}
<pre>
Unsigned Lah numbers up to n==12
n/k 0 1 2 3 4 5 6 7 8 9 10 11 12
0 1
1 0 1
2 0 2 1
3 0 6 6 1
4 0 24 36 12 1
5 0 120 240 120 20 1
6 0 720 1800 1200 300 30 1
7 0 5040 15120 12600 4200 630 42 1
8 0 40320 141120 141120 58800 11760 1176 56 1
9 0 362880 1451520 1693440 846720 211680 28224 2016 72 1
10 0 3628800 16329600 21772800 12700800 3810240 635040 60480 3240 90 1
11 0 39916800 199584000 299376000 199584000 69854400 13970880 1663200 118800 4950 110 1
12 0 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1
The maxiumum of lah(100, _) is: 44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000
</pre>
=={{header|Julia}}==
<lang julia>using Combinatorics
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