Given $F[N,M]=\sum_{m=0}^{N-1}(-1)^{N-1-m}(m+1)^M)/(m!(N-1-m)!)$, show $F[N,N-1]=1$ and $F[N,M]=0$ for $M<N-1$

The function defined by $$ F[N,M]=\sum_{m=0}^{N-1}\frac{(-1)^{N-1-m}(m+1)^M}{m!(N-1-m)!} $$ where $N,M$ are positive integers. I want to show $$ F[N,N-1]=1,\ F[N,M]=0 $$ for $N>2$ and $M<N-1$. Any suggestion will be helpful.