Catalan Number

Very important number series occurring in combinatorics: https://en.wikipedia.org/wiki/Catalan_number

Recurrence relation:

$ C_0 = 1 $

$ C_{n+1} = \sum_{i=0}^{n} C_{i} C_{n-i} $

Formula:

$ C_{n} = \dfrac{(2n)!}{(n+1)! n!} $