|
%I #11 Sep 08 2022 08:45:43
%S 1,40,1598,63760,2540812,101122400,4019487880,159566046400,
%T 6326369025680,250501704284800,9906193528929760,391237707071494400,
%U 15431572025223321280,607873176039216985600,23913706168912873070720
%N a(n) = Hermite(n, 20).
%C The first negative term is a(214). - _Georg Fischer_, Feb 16 2019
%H G. C. Greubel, <a href="/A158703/b158703.txt">Table of n, a(n) for n = 0..675</a>
%F From _G. C. Greubel_, Jul 13 2018: (Start)
%F E.g.f.: exp(40*x - x^2).
%F a(n) = 40*a(n-1) - 2*(n-1)*a(n-2). (End)
%t Table[HermiteH[n, 20], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[40*x - x^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 13 2018 *)
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(40*x - x^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 13 2018
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - x^2))) \\ _G. C. Greubel_, Jul 13 2018
%o (PARI) for(n=0,30, print1(polhermite(n, 20), ", ")) \\ _G. C. Greubel_, Jul 13 2018
%K sign
%O 0,2
%A _N. J. A. Sloane_, Nov 11 2009
|
