#!/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;
}