Calculate the n-th Catalan number

calc_catalan.py

from __future__ import division
import sys

def calc_mod(n, m):
	''' Calculate the n-th Catalan mod m'''
	res = 1
	tmp = 0
	for k in xrange(2, n + 1):
		tmp = ((n + k) / k) % m
		res %= m
		res *= tmp
	return res

# Optimize factorial using memoization
memo_dict = {}

def factorial(n):
	''' Calculate the factorial of n '''
	if n <= 1:
		return 1
	if n in memo_dict:
		return memo_dict[n]
	memo_dict[n] = factorial(n - 1) * n
	return memo_dict[n]

def calc(n):
	''' Calculate the n-th Catalan number '''
	numerator = factorial(2 * n)
	denominator = (factorial(n + 1)) * (factorial(n))
	return numerator / denominator

def main(args):
	if int(args[0]) % 2 != 0:
		print 'Error: please enter an even number'
		return
	if len(args) == 2:
		ans = calc_mod(int(args[0]) // 2, int(args[1]))
	else:
		ans = calc(int(args[0]) // 2)
	print 'The Answer is: %d' % ans
	return

if __name__ == '__main__':
	if len(sys.argv) < 2:
		print 'Usage: python calc_catalan.py num [mod]'
		sys.exit(1)
	main(sys.argv[1:])