The problem I am facing is: Suppose we have a diagonal lattice path which is defined over a $x-y$ coordinate plane. We can go either from $(i,j)$ to $(i+1,j+1)$ or from $(i,j)$ to $(i+1,j-1)$. Then the number of paths from $(0,0)$ to $(m,n)$ is ${m\choose\frac{m-n}{2}}$. Now show that the number of paths from $(0,0)$ to $(n,3)$ that go below $y=-1$ is ${n\choose\frac{n+7}{2}}$.
I have no idea how the formula is obtained. Any help please?