  The Catalan number has a lot of interpretations and one of them is the number
of Dyck paths. A Dyck path is a lattice path from $(0,0)$ to $(n,n)$ which is
below the diagonal line $y=x$. One way to generalize the definition of Dyck
path is to change the end point of Dyck path, i.e. we define (generalized) Dyck
path to be a lattice path from $(0,0)$ to $(m,n) \in \mathbb{N}^2$ which is
below the diagonal line $y=\frac{n}{m}x$, and denote by $C(m,n)$ the number of
Dyck paths from $(0,0)$ to $(m,n)$. In this paper, we give a formula to
calculate $C(m,n)$ for arbitrary $m$ and $n$.
