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%I #11 Sep 08 2022 08:45:43
%S 1,38,1442,54644,2067820,78140008,2948642104,111110719856,
%T 4180926365072,157097430355040,5894445678920224,220846987191867712,
%U 8262507708354728128,308674965224874843776,11514823478128021132160
%N a(n) = Hermite(n, 19).
%C The first negative term is a(194). - _Georg Fischer_, Feb 16 2019
%H G. C. Greubel, <a href="/A158702/b158702.txt">Table of n, a(n) for n = 0..680</a>
%F From _G. C. Greubel_, Jul 13 2018: (Start)
%F E.g.f.: exp(38*x - x^2).
%F a(n) = 38*a(n-1) - 2*(n-1)*a(n-2). (End)
%t Table[HermiteH[n, 19], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[38*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(38*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(38*x - x^2))) \\ _G. C. Greubel_, Jul 13 2018
%o (PARI) for(n=0,30, print1(polhermite(n, 19), ", ")) \\ _G. C. Greubel_, Jul 13 2018
%K sign
%O 0,2
%A _N. J. A. Sloane_, Nov 11 2009
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