A Note on Generalized Narayana Numbers

Abstract

We give a simple proof that the the number of Dyck paths of semilength $n$ with $i$ returns to ground level and $j$ peaks is the generalized Narayana number $\frac{i}{n}\left(\genfrac{}{}{0ex}{}{n}{j}\right)\left(\genfrac{}{}{0ex}{}{n-i-1}{j-i}\right)$.

4 pages