Closed form for $\sum_{p=0}^{i} \binom{a}{p} \binom{b}{i-p} \binom{b+c -(i-p)}{m-i}$

Question

$a,b,c,i,m$ are all integers. Does there exist a closed form for $\sum_{p=0}^{i} \binom{a}{p} \binom{b}{i-p} \binom{b+c -(i-p)}{m-i}$?