import math


def _lattice_path(down, right):
    """Shortest paths using binomial coefficients.

    Binomial[2n, n] or  (2n)!/(n!)^2

    More info can be found here:
      * https://www.robertdickau.com/manhattan.html

    :return:  Number of paths.
    """
    return math.factorial(down + right) // (math.factorial(down) ** 2)