 Narayana number

The number $N(n,k)=\frac{1}{n}\left(\genfrac{}{}{0ex}{}{n}{k}\right)\left(\genfrac{}{}{0ex}{}{n}{k-1}\right)$ counts Dyck paths of semilength $n$ with exactly $k$ peaks, for $1\le k\le n$. Summing over $k$ gives the $n$th Catalan number.

The Narayana numbers are a sequence of numbers that appear in combinatorial mathematics and are related to various counting problems, including those involving paths and combinations.