A158545 - OEIS

%I #13 Sep 08 2022 08:45:43

%S 1,28,782,21784,605260,16773008,463591624,12779289376,351329819792,

%T 9632766324160,263393520320224,7182363242483072,195311513342481088,

%U 5296345655769876736,143219579014652040320,3861850534048700580352,103835227582924055040256

%N a(n) = Hermite(n,14).

%C First negative term is a(109). - _Georg Fischer_, Feb 15 2019

%H G. C. Greubel, <a href="/A158545/b158545.txt">Table of n, a(n) for n = 0..703</a>

%F From _G. C. Greubel_, Jul 13 2018: (Start)

%F E.g.f.: exp(28*x - x^2).

%F a(n) = 28*a(n-1) - 2*(n-1)*a(n-2). (End)

%t Table[HermiteH[n, 14], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[28*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(28*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(28*x - x^2))) \\ _G. C. Greubel_, Jul 13 2018

%o (PARI) for(n=0,30, print1(polhermite(n, 14), ", ")) \\ _G. C. Greubel_, Jul 13 2018

%K sign

%O 0,2

%A _N. J. A. Sloane_, Nov 11 2009