A somewhat low-level implementation of the constant space, linear time change counting algorithm. (By low-level, I mean something that could be straightforwardly translated to C if I actually knew C.)

change.py

#!/usr/bin/env python3

def ways(amount, coins):

    size   = sum(coins) + len(coins)
    starts = [ i + sum(coins[:i]) for i in range(len(coins)) ]
    data   = [ i in starts for i in range(size) ]

    for offset in range(1, amount + 1):
        prev = 0
        for s, c in zip(starts, coins):
            prev = data[(s-offset) % size] = prev + data[(s+c-offset) % size]

    # And there's the answer. Ta Da!
    return data[(starts[-1] - amount) % size]

if __name__ == '__main__':

    from sys import argv

    amount = int(argv[1])
    coins  = [ int(x) for x in argv[2:] ]

    print(ways(amount, coins))