program pi
  use math_mod, only: fact, qp ! integer, parameter :: qp = selected_real_kind(33, 4931)

  implicit none
  real(qp) :: n, k, A, fact3, reverse_pi

  reverse_pi = 0.0_qp

  k = 30.0_qp
  A = 426880.0_qp*sqrt(10005.0_qp)

  do n = 0, int(k)
     fact3 = fact(n)*fact(n)*fact(n)
     reverse_pi = reverse_pi + (fact(6*n)*545140134.0_qp*n+13591409.0_qp)/(fact(3*n)*fact3*(-262537412640768000.0_qp)**n)
  end do

  write(*,'(f103.100)') A/reverse_pi
end program pi