constant @factorial = 1, |[\*] 1..*;
sub Lah (Int \n, Int \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 $mx = (1..$upto).map( { Lah($upto, $_) } ).max.chars;
put 'Unsigned Lah numbers: L(n, k):';
put 'n\k', (0..$upto)».fmt: "%{$mx}d";
for 0..$upto -> $row {
$row.fmt('%-3d').print;
put (0..$row).map( { Lah($row, $_) } )».fmt: "%{$mx}d";
}
say "\nMaximum value from the L(100, *) row:";
say (^100).map( { Lah 100, $_ } ).max;
Output:
Unsigned Lah numbers: L(n, k):
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
Maximum value from the L(100, *) row:
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000