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A277280 Maximal coefficient in Hermite polynomial of order n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

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: A098204 A307635 A323453 * A095197 A333302 A321532

Adjacent sequences:  A277277 A277278 A277279 * A277281 A277282 A277283

KEYWORD

nonn

AUTHOR

Vladimir Reshetnikov, Oct 08 2016

STATUS

approved

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Last modified August 9 12:53 EDT 2020. Contains 336323 sequences. (Running on oeis4.)