https://oeis.org/A000110

distinct_ball

class distinct_ball_memo(dict):

    def __missing__(self, key):
        m, n = key
        if n == 0:
            return 1
        self[key] = m * self[(m, n-1)] + self[(m+1, n-1)]
        return self[key]

def distinct_ball(n):
    return distinct_ball_memo()[(0, n)]

def test_distinct_ball():
    for i in range(1, 21):
        print i, distinct_ball(i)

if __name__ == '__main__':
    test_distinct_ball()