How do I prove $\displaystyle c(n+1, m+1) = \sum_{k=0}^{n} c(n, k) \binom{k}{m}$
The base case is easy to show, but for the induction step do I assume $\displaystyle c(n, m+1) = \sum_{k=0}^{n-1} c(n-1, k) \binom{k}{m}$ is true? and then try to get to $\displaystyle c(n+1, m+1) = \sum_{k=0}^{n} c(n, k) \binom{k}{m}$?
Edit: I am assuming that we want to induct on n.