DouKaku?

use strict;
use warnings;

use bignum;

use List::Util qw/reduce/;
use Memoize;

sub fract
{
  $_[0] == 0 || $_[0] == 1 ? 1 :
  $_[0] * fract($_[0]-1);
}
memoize(q/fract/);

my $N = 32;

print 6 * reduce {
  no warnings qw/once/;
  $a + $b
} map {
  fract(2 * $_) /
  ((2 ** (4 * $_ + 1)) * (fract($_) ** 2) * (2 * $_ + 1))
} 0 .. $N;