A285270 a(n) = H_n(n), where H_n is the physicist's n-th Hermite polynomial.

1, 2, 14, 180, 3340, 80600, 2389704, 83965616, 3409634960, 157077960480, 8093278209760, 461113571640128, 28784033772836544, 1953535902100115840, 143219579014652040320, 11279408109860685024000, 949705205977314865582336, 85131076752851318807814656, 8094279370190580822082014720

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Wikipedia, Hermite polynomial

Formula

a(n) ~ exp(-1/4) * 2^n * n^n. - Vaclav Kotesovec, Nov 07 2021

Example

Knowing that H_3(x) = 8x^3-12x, a(3) = H_3(3) = 8*3^3-12*3 = 180.

Mathematica

Table[HermiteH[n, n], {n, 0, 18}] (* Michael De Vlieger, May 25 2017 *)

Prog

(PARI) a(n) = polhermite(n, n); \\ Michel Marcus, May 25 2017
(Python)
from sympy import hermite
def a(n): return hermite(n, n) # Indranil Ghosh, May 25 2017

Crossrefs

Cf. A089466 (probabilist's variant).

Cf. A349066, A349067, A349068, A349069.

Sequence in context: A252727 A375868 A381389 * A109520 A370054 A210097

Adjacent sequences: A285267 A285268 A285269 * A285271 A285272 A285273

Keyword

nonn

Author

Natan Arie Consigli, May 24 2017

Extensions

More terms from Michel Marcus, May 25 2017

Status

approved