Ballot Paths Never Behind

Problem

The number of monotone paths from (0, 0) to (n, n) that never go above the diagonal is the Catalan number C(2n, n) / (n + 1).

Given n, return the count.

Hint

The reflection principle gives 1 / (n + 1) of all paths.

case 1

in: [1]

expected: 1

case 2

in: [3]

expected: 5

case 3

in: [4]

expected: 14

Starter codePython

def ballot_paths_never_behind(n):
    # Your code here
    pass

3 test cases · run your code against them in the editor