%I #15 Jun 09 2024 14:39:09
%S 1,36,1294,46440,1664076,59535216,2126627016,75844149984,
%T 2700616621200,96008691963456,3407701811502816,120757091374832256,
%U 4272285849640899264,150904120394076399360,5321468902096086996096,187347565104424992677376
%N a(n) = Hermite(n, 18).
%C The first negative term is a(175). - _Georg Fischer_, Feb 15 2019
%H G. C. Greubel, <a href="/A158700/b158700.txt">Table of n, a(n) for n = 0..685</a>
%F From _G. C. Greubel_, Jul 13 2018: (Start)
%F E.g.f.: exp(36*x - x^2).
%F a(n) = 36*a(n-1) - 2*(n-1)*a(n-2). (End)
%t Table[HermiteH[n, 18], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[36*x - x^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 13 2018 *)
%t nxt[{n_,a_,b_}]:={n+1,b,36b-2a*n}; NestList[nxt,{1,1,36},20][[;;,2]] (* _Harvey P. Dale_, Jun 09 2024 *)
%o (PARI) a(n)=polhermite(n,18) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - x^2))) \\ _G. C. Greubel_, Jul 13 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(36*x - x^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 13 2018
%K sign
%O 0,2
%A _N. J. A. Sloane_, Nov 11 2009