How find this sum $\sum_{k=0}^{p}t^k\binom{n}{k}\binom{m}{p-k}$ Find the closed form
$$\sum_{k=0}^{p}t^k\binom{n}{k}\binom{m}{p-k}$$
since
$$\binom{n}{k}\binom{m}{p-k}=\dfrac{n!}{(n-k)!k!}\cdot\dfrac{m!}{(p-k)!(m-p+k)!}$$
then I can't 

Hint: this equation represents coefficient of $x^p$ in $$(1+tx)^n×(1+x)^m$$
