A277281 Maximal coefficient (ignoring signs) in Hermite polynomial of order n.

1, 2, 4, 12, 48, 160, 720, 3360, 13440, 80640, 403200, 2217600, 13305600, 69189120, 484323840, 2905943040, 19372953600, 131736084480, 846874828800, 6436248698880, 42908324659200, 337903056691200, 2477955749068800, 18997660742860800, 151981285942886400

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 (ignoring signs) is 160, so a(5) = 160.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..715
• Eric Weisstein's World of Mathematics, Hermite Polynomial.
• Wikipedia, Hermite polynomials.

Crossrefs

Cf. A059343, A277280 (with signs).

Programs

Mathematica

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

PARI

a(n) = vecmax(apply(x->abs(x), Vec(polhermite(n)))); \\ Michel Marcus, Oct 09 2016

Python

from sympy import hermite, Poly
def a(n): return max(map(abs, Poly(hermite(n, x), x).coeffs())) # Indranil Ghosh, May 26 2017