lets say i have a function where:
$[p,c,n,k] \in \mathbb{Z}$ defined some way in this function
$ f(x) = \sum_{q=0}^{n} \sum_{v=1}^{k-q+1}\frac{c(k+1-v)!(p-k)!}{(k+1-v-q)!q!(p-k-q)!}x^{k-v+1-q} = \sum_{q=0}^{n} \sum_{v=1}^{k-q+1}\frac{c(k+1-v)_q (p-k)_q}{q!}x^{k-v+1-q} $
Where $(d)_q$ is a falling factorial
Does such a function already exist? It seems like a finite hyper-geometric series