login
a(n) = Hermite(n,12).
1

%I #14 Sep 08 2022 08:45:43

%S 1,24,574,13680,324876,7687584,181253256,4257827136,99650305680,

%T 2323482102144,53969864949216,1248807116738304,28784033772836544,

%U 660845439746357760,15111905675818836096,344182063906754049024,7807012363487532093696,176354470678684640679936

%N a(n) = Hermite(n,12).

%C The first negative term is a(82). - _Georg Fischer_, Feb 15 2019

%H G. C. Greubel, <a href="/A158538/b158538.txt">Table of n, a(n) for n = 0..711</a>

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

%F E.g.f.: exp(24*x - x^2).

%F a(n) = 24*a(n-1) - 2*(n-1)*a(n-2). (End)

%t Table[HermiteH[n, 12], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[24*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(24*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(24*x - x^2))) \\ _G. C. Greubel_, Jul 13 2018

%o (PARI) for(n=0,30, print1(polhermite(n, 12), ", ")) \\ _G. C. Greubel_, Jul 13 2018

%K easy,sign

%O 0,2

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