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def factorielle(n):
    if n <= 1 : return 1
    else : return n * factorielle(n-1)

def binomial_fact(n, k):
    assert k >= 0 and n >= 0
    return factorielle(n)/(factorielle(k)*factorielle(n-k))

def binomial_pascal (n, k):
    assert k >= 0 and n >= 0
    if k == n or k==0:
        return 1
    elif k>n:
        return 0
    else:
        return binomial_pascal(n-1,k)+binomial_pascal(n-1,k-1)

def binomial_capitaine(n,k):
    assert k >= 0 and n >= 0
    if k == n or k==0:
        return 1
    elif k>n:
        return 0
    else:
        return binomial_capitaine(n-1,k-1)*n/k

if __name__ == "__main__" :
    assert factorielle(4) == 24 and factorielle(6) == 720 and factorielle(-2) 
    == 1
    assert binomial_fact(2,1) == 2 and binomial_fact(4,2) == 6 and binomial_fact
    (5,3) == 10 and binomial_fact(6,3) == 20
    assert binomial_pascal(2,1) == 2 and binomial_pascal(4,2) == 6 and 
    binomial_pascal(5,3) == 10 and binomial_pascal(6,3) == 20
    assert binomial_capitaine(2,1) == 2 and binomial_capitaine(4,2) == 6 and 
    binomial_capitaine(5,3) == 10 and binomial_capitaine(6,3) == 20