?In Table of Integrals, Series, and Products. Seventh Edition. I.S. Gradshteyn and I.M. Ryzhik, there is 
0.154.3
$$ 
\sum_{k=0}^N (-1)^k {N \choose k}  k^{n-1} =0, N \geq n \geq 1; 0^0 ≡ 1
$$
0.154.4
$$
\sum_{k=0}^N (-1)^k {n \choose k}  k^{n} =(-1)^n n!,  n \geq 0; 0^0 ≡ 1
$$

I would like to know, there is any generalization for 0.154.4 for even higer-power of $k$?
$$
\sum_{k=0}^N (-1)^k {n \choose k}  k^{n+m} =?,  n \geq 0; m\geq0; 0^0 ≡ 1
$$