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A285270 a(n) = H_n(n), where H_n is the physicist's n-th Hermite polynomial. 4
1, 2, 14, 180, 3340, 80600, 2389704, 83965616, 3409634960, 157077960480, 8093278209760, 461113571640128, 28784033772836544, 1953535902100115840, 143219579014652040320, 11279408109860685024000, 949705205977314865582336, 85131076752851318807814656, 8094279370190580822082014720 (list; graph; refs; listen; history; text; internal format)
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: A336635 A208195 A252727 * A109520 A210097 A230991

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

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)