Can we solve this particular function through dynamic programming?

Question

F(M)= (kC1 * (n-k)C(M-1)) + (kC3 * (n-k)C(M-2)) + ...

F(M+1)= (kC1 * (n-k)C(M)) + (kC3 * (n-k)C(M-1)) + ...

we have to find this for all M <= n. 1<=n <= 1