# Combinatorial Math

#### migvas99

##### New member
I'm stuck in this question. It seems so easy, but I can't see it and at this point I spent too many time on it to be able to look at it with fresh eyes.

For each $$\displaystyle n\in N$$, consider:
$$\displaystyle S_n=\sum_{k=0}^n (-1)^k\binom{n}{k}k^n$$

Show:
$$\displaystyle S_n=-nS_{n-1}+n\sum_{k=0}^n (-1)^k\binom{n}{k}k^{n-1},\quad n\ge1$$

Any helps is greatly appreciated!