integration - Does this integral have an analytical solution?

Looking for a generic analytical solution to the following integral:

$\int^{+\infty}_{-\infty} x^k H_n(x) e^{-x^2} dx$

in terms of $k$ and $n$, there's probably a $\sqrt{\pi}$ in there somewhere. Where $k$ and $n$ are integers and $H_n$ is the $n^{\text{th}}$ order Hermit polynomial. It seems so simple so I think there should be one. Anyone know of a paper or source that has the analytical solution? Cheers Guys!