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A158542 a(n) = Hermite(n,13). 1

%I

%S 1,26,674,17420,448876,11531416,295328056,7540152464,191909371280,

%T 4869001213856,123139662877216,3104251210530496,78001458890494144,

%U 1953535902100115840,48763895523450164096,1213162278350901022976,30079302371419921674496,743240668749689130801664

%N a(n) = Hermite(n,13).

%C First negative term is a(95). - _Georg Fischer_, Feb 15 2019

%H G. C. Greubel, <a href="/A158542/b158542.txt">Table of n, a(n) for n = 0..706</a>

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

%F E.g.f.: exp(26*x - x^2).

%F a(n) = 26*a(n-1) - 2*(n-1)*a(n-2). (End)

%t Table[HermiteH[n, 13], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[26*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(26*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(26*x - x^2))) \\ _G. C. Greubel_, Jul 13 2018

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

%K sign

%O 0,2

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

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Last modified October 18 05:22 EDT 2019. Contains 328146 sequences. (Running on oeis4.)