sub factln
{
  my $x = (shift) + 1;
  my $tmp = $x + 5.5;
  $tmp -= ($x + .5) * log($tmp);
  my $ser = 1.000000000190015
         + 76.18009172947146    / ++$x
         - 86.50532032941677    / ++$x
         + 24.01409824083091    / ++$x
         -  1.231739572450155   / ++$x
         +  0.12086509738661e-2 / ++$x
         -  0.5395239384953e-5  / ++$x;
  return log(2.5066282746310005*$ser/($x-6)) - $tmp;
}