Calculate binomial coefficients via Pascal's triangle

binomial_coefficients.py

def next_row(prev_row):
        row = [prev_row[0]] * (len(prev_row) + 1)
        for idx in range(len(prev_row) - 1):
            row[idx + 1] = (prev_row[idx] + prev_row[idx + 1])
        return row

def binomial(n, k, cache=None):
    """ Calculates binomial coefficients using Pascal's triangle.
  
        0             1
        1            1 1
        2           1 2 1
        3          1 3 3 1
        4         1 4 6 4 1
        ...
        
    Use `cache` for reusing previous calculation results.
    """
    if k == 0 or k == n:
        return 1
    if k == 1 or k == n - 1:
        return n

    cache = cache or [[1]]
    while len(cache) <= n:
        cache.append(next_row(cache[-1]))
    return cache[n][k]

if __name__ == '__main__':
    c = None  # = [] uncomment it to speed up execution.
    for n in range(150):
        for k in range(n + 1):
            print('n={n}, k={k} -> {b}'.format(n=n, k=k, b=binomial(n, k, c)))