%I #12 Sep 08 2022 08:45:44
%S 1,16,-466,-30560,520396,96583616,-333291704,-423732891776,
%T -5095269996400,2365956862955776,70964374243899616,
%U -15946778562638308864,-818747517247263692096,125062929190742088924160,9685771063934690436799616,-1109163751237065987856615424
%N Numerator of Hermite(n, 8/19).
%H G. C. Greubel, <a href="/A159646/b159646.txt">Table of n, a(n) for n = 0..396</a>
%F From _G. C. Greubel_, Jul 10 2018: (Start)
%F a(n) = 19^n * Hermite(n, 8/19).
%F E.g.f.: exp(16*x - 361*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,8/19],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 20 2011 *)
%t Table[19^n*HermiteH[n, 8/19], {n,0,50}] (* _G. C. Greubel_, Jul 10 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,8/19)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 10 2018
%Y Cf. A159564, A159618.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009