Is there any way that I could simplify the following expression?
$$\sum_{r = 0}^{n} {{n}\choose{r}}r^k(-1)^r$$
where $n,k$ are natural numbers (and in my particular problem, $k \gg n$, so maybe some sort of asymptotic behaviour?)
I tried finding some sort of generating function (without any luck, though I haven't really learnt much about them yet), looking at differences between terms, but I haven't really been able to make any progress whatsoever.
