# Sum of binomial coefficients and powers

The following identity is true for $n\geq1$:

$$n!=\sum_{k=1}^n (-1)^{n-k} {n\choose k} k^{n}$$

You can obtain it from the equation in this question by setting the variables equal to 1.

I was wondering if anyone could come up with an elementary proof, maybe a counting argument? (I've found this rather tricky)

• Turns out this is a duplicate of this question, sorry – Blunka Feb 17 '15 at 10:16