Lah numbers: Difference between revisions
Added Perl example
SqrtNegInf (talk | contribs) (Added Perl example) |
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The maxiumum of lah(100, _) is: 44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000
</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
{{trans|Perl 6}}
<lang perl>use strict;
use warnings;
use feature 'say';
use ntheory qw(factorial);
use List::Util qw(max);
sub Lah {
my($n, $k) = @_;
return factorial($n) if $k == 1;
return 1 if $k == $n;
return 0 if $k > $n;
return 0 if $k < 1 or $n < 1;
(factorial($n) * factorial($n - 1)) / (factorial($k) * factorial($k - 1)) / factorial($n - $k)
}
my $upto = 12;
my $mx = 1 + length max map { Lah(12,$_) } 0..$upto;
say 'Unsigned Lah numbers: L(n, k):';
print 'n\k' . sprintf "%${mx}s"x(1+$upto)."\n", 0..1+$upto;
for my $row (0..$upto) {
printf '%-3d', $row;
map { printf "%${mx}d", Lah($row, $_) } 0..$row;
print "\n";
}
say "\nMaximum value from the L(100, *) row:";
say max map { Lah(100,$_) } 0..100;</lang>
{{out}}
<pre>Unsigned Lah numbers: L(n, k):
n\k 0 1 2 3 4 5 6 7 8 9 10 11
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
Maximum value from the L(100, *) row:
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000</pre>
=={{header|Perl 6}}==
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