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%I #12 Sep 08 2022 08:45:43
%S 1,8,-98,-3376,20620,2352608,2118664,-2269785664,-20560850288,
%T 2777155418240,52194963065824,-4081432073022208,-125662880767476032,
%U 6929000903815364096,320078034126827436160,-13154349776838626280448,-883024421142899680112384
%N Numerator of Hermite(n, 4/9).
%H G. C. Greubel, <a href="/A159232/b159232.txt">Table of n, a(n) for n = 0..450</a>
%F From _G. C. Greubel_, Jun 28 2018: (Start)
%F a(n) = 9^n * Hermite(n, 4/9).
%F E.g.f.: exp(8*x-81*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/9)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,4/9],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2011*)
%o (PARI) a(n)=numerator(polhermite(n,4/9)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 28 2018
%Y Cf. A159030, A159197.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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