Hermite polynomial/Addendum

The following is a list of Hermite polynomials H_n(x) through n = 12. The polynomials are standardized such that the coefficient of xⁿ = 2ⁿ.

${\begin{aligned}H_{0}(x)&=1\\H_{1}(x)&=2\,x\\H_{2}(x)&=4\,x^{2}-2\\H_{3}(x)&=8\,x^{3}-12\,x\\H_{4}(x)&=16\,x^{4}-48\,x^{2}+12\\H_{5}(x)&=32\,x^{5}-160\,x^{3}+120\,x\\H_{6}(x)&=64\,x^{6}-480\,x^{4}+720\,x^{2}-120\\H_{7}(x)&=128\,x^{7}-1344\,x^{5}+3360\,x^{3}-1680\,x\\H_{8}(x)&=256\,x^{8}-3584\,x^{6}+13440\,x^{4}-13440\,x^{2}+1680\\H_{9}(x)&=512\,x^{9}-9216\,x^{7}+48384\,x^{5}-80640\,x^{3}+30240\,x\\H_{10}(x)&=1024\,x^{10}-23040\,x^{8}+161280\,x^{6}-403200\,x^{4}+302400\,x^{2}-30240\\H_{11}(x)&=2048\,x^{11}-56320\,x^{9}+506880\,x^{7}-1774080\,x^{5}+2217600\,x^{3}-665280\,x\\H_{12}(x)&=4096\,x^{12}-135168\,x^{10}+1520640\,x^{8}-7096320\,x^{6}+13305600\,x^{4}-7983360\,x^{2}+665280\end{aligned}}$