A349068 a(n) = H(n, 2*n), where H(n,x) is n-th Hermite polynomial.

1, 4, 62, 1656, 62476, 3041200, 181253256, 12779289376, 1040259450512, 96008691963456, 9906193528929760, 1129945699713533824, 141183268107518731968, 19176614030629200880384, 2813353012562289110458496, 443345766248682440278848000, 74687922008799389150557901056

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Eric Weisstein's World of Mathematics, Hermite Polynomial.

Wikipedia, Hermite polynomial.

Formula

a(n) ~ exp(-1/16) * 4^n * n^n.

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * ( n! / (k! * (n-2k)!) ) * (4n)^(n-2k), for n>0. - Bernard Schott, Nov 07 2021

Maple

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

Mathematica

Table[HermiteH[n, 2*n], {n, 0, 20}]

Prog

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

Crossrefs

Cf. A285270, A349066, A349069.

Sequence in context: A241997 A332694 A277392 * A054958 A191300 A087613

Adjacent sequences: A349065 A349066 A349067 * A349069 A349070 A349071

Keyword

nonn

Author

Vaclav Kotesovec, Nov 07 2021

Status

approved