A349067 a(n) = H(3*n, n), where H(n,x) is n-th Hermite polynomial.

1, -4, -824, -406944, 854857408, 36727035808000, 1350597603460566528, 70169228831160001808384, 5261285254051930823802720256, 556216363355718012207356567863296, 80574670961706857240366003306352640000, 15573012689517863187913236259514917169004544

Offset: 0

Author

Vaclav Kotesovec, Nov 07 2021

Keywords

• sign

Comments

In general, for k>=1, H(k*n,n) ~ exp(-k^2/4) * 2^(k*n) * n^(k*n).

Links

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

Crossrefs

Cf. A285270, A349066, A349069.

Programs

Maple

a:= n-> simplify(HermiteH(3*n, n)):
seq(a(n), n=0..20);  # Alois P. Heinz, Nov 07 2021

Mathematica

Table[HermiteH[3*n, n], {n, 0, 12}]

PARI

a(n) =  polhermite(3*n, n); \\ Michel Marcus, Nov 07 2021

Formula

a(n) ~ exp(-9/4) * 2^(3*n) * n^(3*n).