Calculating Integrals with Hermite Polynomials

[alejandrito29]

Hello , i need to calculate the following integral

$$\int_{-\infty}^{\infty} x^4 H(x)^2 e^{-x^2} dx$$

i tried using the recurrence relation, but i don't go the answer

 

[vanhees71]

What's $H$? The Hermite polynomials have an index, i.e., $H_n$ with $n \in \mathbb{N}_0$.