Narayana numbers

The Narayana numbers $N (n, k)$ are the number of Dyck paths with $k$ peaks.

It is given explicitly by

N (n, k) = \frac{1}{n} (\binom{n}{k}) (\binom{n}{k - 1})

Examples

It is symmetric: $N (n, k) = N (n, n + 1 - k)$
$N (n, k)$ is the number of plane binary trees with $n$ vertices and $k - 1$ left edges.