https://www.geeksforgeeks.org/program-nth-catalan-number/?ref=lbp

Catalan Number

The Catalan number $C_n$ equals the number of valid parenthesis expressions that consist of $n$ left parentheses and $n$ right parentheses.

Catalan numbers can be calculated using the formula: $C_n=\sum _{i=0}^{n-1}{C}_i{C}_{n-i-1}$ Catalan numbers can also be calculated using binomial coefficients:

$C_n=\frac{1}{n+1}\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$