Simplify a equation

Question

I have a problem simplifying the summation here:

$$ \sum_{x=0}^{n}\sum_{y=0}^{x} {n\choose{x}} {x\choose{y}} y!(x-y)! $$

The last three terms can be simplified to x!, so the current summation becomes:

$$ \sum_{x=0}^{n}\sum_{y=0}^{x} {n\choose{x}} x! = \sum_{x=0}^{n}{n\choose{x}}(x+1)! $$

Then I get stuck here, it seems it should relate to $e$, please inspire me if any one knows the answer.

Thanks for the help.

Answer 1

Mathematica says:

$$\frac{1}{n+1}+\frac{e n \Gamma (n+2,1)}{n+1}.$$