Hermite Polynomial Recurrence Question

[timman_24]

Homework Statement

I need to find an expression for:
$y^{2}H(y)$

I know how to find:
$yH(y)$
with:
$yH(y)=\frac{1}{2}H_{n+1}(y)+nH_{n-1}(y)$

I looked through the miscellaneous relations but nothing stuck out to me. Can someone give me some guidance on how to go about finding a relation? I assume I do not simply multiply both sides by y!

Thanks

 

[vela]

Multiply both sides by y, then expand out the righthand side.