DouKaku?

use strict;
use warnings;

use bignum;

use Memoize;

sub fract
{
  my $n = shift;
  $n == 0 || $n == 1 ? 1 :
  $n * fract($n-1);
}
sub f
{
  my $n = shift;
  $n < 0 ? 0 :
  fract(2 * $n) /
  ((2 ** (4 * $n + 1)) * (fract($n) ** 2) * (2 * $n + 1)) +
  f($n-1);
}
memoize(q/fract/);
memoize(q/f/);

my $N = 1024;

print "@{[6 * f($_)]}\n" for 1 .. $N;