A158727 - OEIS

%I #11 Sep 08 2022 08:45:43

%S 1,42,1762,73836,3090540,129211992,5395998264,225081383184,

%T 9377874118032,390269410826400,16222513520584224,673540179648009408,

%U 27931792247763542208,1156970310094516546944,47866526425527842874240

%N a(n) = Hermite(n, 21).

%C The first negative term is a(235). - _Georg Fischer_, Feb 16 2019

%H G. C. Greubel, <a href="/A158727/b158727.txt">Table of n, a(n) for n = 0..670</a>

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

%F E.g.f.: exp(42*x - x^2).

%F a(n) = 42*a(n-1) - 2*(n-1)*a(n-2). (End)

%t Table[HermiteH[n, 21], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[42*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(42*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(42*x - x^2))) \\ _G. C. Greubel_, Jul 13 2018

%o (PARI) for(n=0,30, print1(polhermite(n, 21), ", ")) \\ _G. C. Greubel_, Jul 13 2018

%K sign

%O 0,2

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