\[\sum_{\ell=0}^{n}\genfrac{(}{)}{0.0pt}{}{n}{\ell}H_{2\ell}\left(x\right)H_{2n-%
2\ell}\left(y\right)=(-1)^{n}2^{2n}n!L_{n}\left(x^{2}+y^{2}\right).\]