Binomial coefficient in Python

binom.py

# Python script to calculate the binomial coefficient C(n, k)
# where n is an integer or floating point number and k is an integer.
#
# We use the following general definition:
#    C(n, k) = n(n-1)(n-2)...(n-k+1) / k!  if k >= 0, 
#              0 if k < 0.
#   
# For n < 0, we use the negative binomial identity
#    C(n, k) = (-1)^k * C(k - n - 1, k)
#
# We also use the symmetric identity
#    C(n, k) = C(n, n - k)
# when n > 0 and n/2 < k < n.
#
# Reference: "Concrete Mathematics" by Ronald Graham, Donald Knuth, and Oren Patashnik.

def binomial_coefficient(n, k):
    if not isinstance(k, int):
        raise ValueError('The second argument must be an integer.')
    if k < 0:
        return 0
    if n < 0:
        return (-1) ** k * binomial_coefficient(k - n - 1, k)
    if k > n:
        return 0
    if k > n // 2:
        k = n - k
    result = 1
    for i in range(k):
        result = result * (n - i) // (i + 1)
    return result