Sum of powers of natural numbers
There is no factorial in the formula, there are binomial coefficients. If you look up the definition carefully, you will note that for nonnegative integers $n,k$ we have
$${n \choose k} := \begin{cases} \frac{n!}{k!(n-k)!}, & k \leq n \\ 0 & else\end{cases}.$$
Thus, you will not run into trouble as there will be no factorials in your case.