

def binomial_coefficients(n):
    'Return a dictionary containing pairs :math:`{(k1,k2) : C_kn}` where\n    :math:`C_kn` are binomial coefficients and :math:`n=k1+k2`.\n    Examples\n    ========\n\n    >>> from sympy.ntheory import binomial_coefficients\n    >>> binomial_coefficients(9)\n    {(0, 9): 1, (1, 8): 9, (2, 7): 36, (3, 6): 84,\n     (4, 5): 126, (5, 4): 126, (6, 3): 84, (7, 2): 36, (8, 1): 9, (9, 0): 1}\n\n    See Also\n    ========\n\n    binomial_coefficients_list, multinomial_coefficients\n    '
    d = {
        (0, n): 1,
        (n, 0): 1,
    }
    a = 1
    for k in range(1, ((n // 2) + 1)):
        a = ((a * ((n - k) + 1)) // k)
        d[(k, (a - k))] = d[((n - k), k)] = a
    return d

dataset/ETHPy150Open sympy/sympy/sympy/ntheory/multinomial.py binomial_coefficients/VarMisuse@86/325 `n`->`a`