Catalan Number

Problem

Compute the n-th Catalan number, which counts balanced bracket sequences and Dyck paths:

C_n = C(2n, n) / (n + 1).

Return 0 for negative n.

Hint

Use integer division after math.comb to stay exact.

case 1

in: [0]

expected: 1

case 2

in: [3]

expected: 5

case 3

in: [5]

expected: 42

case 4

in: [10]

expected: 16796

Starter codePython

import math


def catalan_number(n):
    # Your code here
    pass

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