For given a nonnegative integer number $N$ and $M$, I want to find how many cases exist where $N$ can be expressed as the sum of $M$ integers.
For example, if $N=5$ and $M=2$, there are only three cases, i.e., $(0,5)$, $(1,4)$, and $(2,3)$.
If $N=5$ and $M=3$, there are only five cases, i.e., $(0,0,5)$, $(0,1,4)$, $(0,2,3)$, $(1,1,3)$, and $(1,2,2)$.
Is there a formula to find the number of cases where $N$ is expressed as the sum of arbitrary $M$ integers?