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%I #22 Jan 07 2023 05:45:02
%S 1,2,4,8,16,120,720,3360,13440,48384,302400,2217600,13305600,69189120,
%T 322882560,2421619200,19372953600,131736084480,790416506880,
%U 4290832465920,40226554368000,337903056691200,2477955749068800,16283709208166400,113985964457164800
%N Maximal coefficient in Hermite polynomial of order n.
%H Vaclav Kotesovec, <a href="/A277280/b277280.txt">Table of n, a(n) for n = 0..710</a>
%H Vaclav Kotesovec, <a href="/A277280/a277280.jpg">Plot of a(n+1)/(a(n)*sqrt(n)) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HermitePolynomial.html">Hermite Polynomial</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hermite_polynomials">Hermite polynomials</a>.
%e 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.
%t Table[Max@CoefficientList[HermiteH[n, x], x], {n, 0, 25}]
%o (PARI) a(n) = vecmax(Vec(polhermite(n))); \\ _Michel Marcus_, Oct 09 2016
%o (Python)
%o from sympy import hermite, Poly
%o def a(n): return max(Poly(hermite(n, x), x).coeffs()) # _Indranil Ghosh_, May 26 2017
%Y Cf. A059343, A277281 (ignoring signs).
%K nonn
%O 0,2
%A _Vladimir Reshetnikov_, Oct 08 2016
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