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Numerator of Hermite(n, 8/19).
2

%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