A277280 Maximal coefficient in Hermite polynomial of order n.

1, 2, 4, 8, 16, 120, 720, 3360, 13440, 48384, 302400, 2217600, 13305600, 69189120, 322882560, 2421619200, 19372953600, 131736084480, 790416506880, 4290832465920, 40226554368000, 337903056691200, 2477955749068800, 16283709208166400, 113985964457164800

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..710

Vaclav Kotesovec, Plot of a(n+1)/(a(n)*sqrt(n)) for n = 1..10000

Eric Weisstein's World of Mathematics, Hermite Polynomial.

Wikipedia, Hermite polynomials.

Example

For n = 5, H_5(x) = 32*x^5 - 160*x^3 + 120*x. The maximal coefficient is 120 (we take signs into account, so -160 < 120), hence a(5) = 120.

Mathematica

Table[Max@CoefficientList[HermiteH[n, x], x], {n, 0, 25}]

Prog

(PARI) a(n) = vecmax(Vec(polhermite(n))); \\ Michel Marcus, Oct 09 2016
(Python)
from sympy import hermite, Poly
def a(n): return max(Poly(hermite(n, x), x).coeffs()) # Indranil Ghosh, May 26 2017

Crossrefs

Cf. A059343, A277281 (ignoring signs).

Sequence in context: A341109 A307635 A323453 * A095197 A333302 A321532

Adjacent sequences: A277277 A277278 A277279 * A277281 A277282 A277283

Keyword

nonn

Author

Vladimir Reshetnikov, Oct 08 2016

Status

approved