$\displaystyle \sum _{n=1}^{\infty }{\frac {n!}{{e}^{{n}^{2}}}}$

I tried the ratio test, from my figuring, I got that it diverges. However, the back of the book says otherwise ;)

I end up getting

$\displaystyle {\frac {n+1}{e}}$

I'm pretty sure that's wrong.