$$ \sum_{k=0}^n \left\{ {n\atop k} \right\} *(x)_k = x^n $$ is well known .
What if the k-th term of LHS summation is divided by $q^k$ where $q$ is some positive constant,
What about
$$ \sum_{k=0}^n[ \left\{ {n\atop k} \right\} *(x)_k ]/(q^k) = ? $$