the_0ne,
I understand that, which is why I said modifying the code would not be difficult to do that. The problem is you seem to want to proceed with using a technique that is producing far more candidates than is necessary. Making a terrible approach more efficient isn't going to make it work.
Cheers  L~R
Update: Even with only pulling unique combinations, it does not take long to get to astronimical numbers as pointed out by kvale earlier. Try out the following code.
#!/usr/bin/perl
use strict;
use warnings;
my $k = $ARGV[0]  50;
my $total = 1;
for my $n ( 1 .. $k  1 ) {
if ( $n > $k  $n ) {
$total += factorial($k, $n + 1) / factorial( $k  $n );
}
else {
$total += factorial($k, $k  $n + 1) / factorial( $n );
}
}
print "Total unique combinations for $k is $total\n";
sub factorial {
my ($n, $max, $total) = @_;
$total = 1;
$max = 0;
return $total if ! $n  $n == $max  1;
@_ = ($n  1, $max, $total * $n);
goto &factorial;
}
