A349069 a(n) = H(n, 3*n), where H(n,x) is n-th Hermite polynomial.

1, 6, 142, 5724, 324876, 23761800, 2126627016, 225081383184, 27498818692752, 3808595968290144, 589662462800129760, 100917872425324633536, 18918488805502510634688, 3855242696428245589623936, 848531650317994634533024896, 200604383862593153678170272000

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..15.

Eric Weisstein's World of Mathematics, Hermite Polynomial.

Wikipedia, Hermite polynomial.

Formula

a(n) ~ exp(-1/36) * 6^n * n^n.

Maple

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

Mathematica

Table[HermiteH[n, 3*n], {n, 0, 20}]

Crossrefs

Cf. A285270, A349067, A349068.

Sequence in context: A363989 A278356 A277419 * A111839 A349076 A037049

Adjacent sequences: A349066 A349067 A349068 * A349070 A349071 A349072

Keyword

nonn

Author

Vaclav Kotesovec, Nov 07 2021

Status

approved