crude combination solution with dynamic programming

01_comb_dp.py

def factorial(n):
    if factorial_array[n] > -1:
        return factorial_array[n]
    else:
        factorial_array[n-1] = factorial(n - 1)
        return n * factorial_array[n-1]


def combination(n, k):
    if k == 0 or n == k:
        return 1
    else:
        return int(factorial(n) / factorial(k) / factorial(n - k))


a = input().split(' ')
if not a[0].isdigit() or len(a) == 1 or not a[1].isdigit():
    print('both n and k should be numbers')
    quit()

n, k = int(a[0]), int(a[1])
if n < 0 or k < 0:
    print('both n and k should be >= 0')
    quit()

factorial_array = [1]
factorial_array = factorial_array + [-1] * n    #fill list with -1 n times

for n2 in range(n + 1):
    for k2 in range(n2 + 1):
        print("{0}C{1} = {2}".format(n2, k2, combination(n2, k2)), end="  ")
    print()