A349066 a(n) = H(2*n, n), where H(n,x) is n-th Hermite polynomial.

1, 2, 76, 14136, 5324432, 3275529760, 2982971060928, 3773262142004096, 6332628384952750336, 13620318069121988018688, 36536710970888029776972800, 119598502032157660592768038912, 469232422933986002753883881312256, 2173747962477936168042899607178059776

Offset: 0

Author

Vaclav Kotesovec, Nov 07 2021

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Hermite Polynomial.
• Wikipedia, Hermite polynomial.

Crossrefs

Cf. A285270, A349067, A349068.

Programs

Maple

a:= n-> simplify(HermiteH(2*n, n)):
seq(a(n), n=0..20);  # Alois P. Heinz, Nov 07 2021

Mathematica

Table[HermiteH[2*n, n], {n, 0, 15}]

PARI

a(n) =  polhermite(2*n, n); \\ Michel Marcus, Nov 07 2021

Formula

a(n) ~ exp(-1) * 2^(2*n) * n^(2*n).