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

Author

Vladimir Reshetnikov, Oct 08 2016

Keywords

• nonn

Examples

			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.
		

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.

Crossrefs

Cf. A059343, A277281 (ignoring signs).

Programs

Mathematica

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

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