A158696 - OEIS

%I #10 Sep 08 2022 08:45:43

%S 1,34,1154,39100,1322476,44651384,1504922296,50631541456,

%T 1700403497360,57003614246944,1907515621443616,63715458844144064,

%U 2124360257029138624,70699077726731255680,2348535276026105088896,77870625208539097863424

%N a(n) = Hermite(n, 17).

%C First negative term is a(157). - _Georg Fischer_, Feb 15 2019

%H G. C. Greubel, <a href="/A158696/b158696.txt">Table of n, a(n) for n = 0..691</a>

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

%F E.g.f.: exp(34*x - x^2).

%F a(n) = 34*a(n-1) - 2*(n-1)*a(n-2). (End)

%t Table[HermiteH[n, 17], {n, 0, 50}] (* or *) With[{nmax = 50}, CoefficientList[Series[Exp[34*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(34*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(34*x - x^2))) \\ _G. C. Greubel_, Jul 13 2018

%o (PARI) for(n=0,30, print1(polhermite(n, 17), ", ")) \\ _G. C. Greubel_, Jul 13 2018

%K sign

%O 0,2

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