Hermite polynomial

$H_n(x):=(-1{)}^n{e}^{\frac{x^2}{2}}\frac{d^n}{d{x}^n}\left(e^{-\frac{x^2}{2}}\right)$.

Explicitly,

$$\begin{array}{rl}{H}_0(x)& =1\\ H_1(x)& =x\\ H_2(x)& =x^2-1\\ H_3(x)& =x^3-3x\\ H_4(x)& =x^4-6x^2+3\\ H_5(x)& =x^5-10x^3+15x\\ H_6(x)& =...\end{array}$$