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%I #13 Sep 08 2022 08:45:43
%S 1,5,-7,-355,-1103,39925,376105,-5785075,-113172895,915114725,
%T 37169367385,-106989875075,-13618566694895,-27008721445675,
%U 5530280137847945,39751307896902125,-2455777926682502975,-32631559276626402875,1172785395732149604025
%N Numerator of Hermite(n, 5/8).
%H G. C. Greubel, <a href="/A159019/b159019.txt">Table of n, a(n) for n = 0..450</a>
%F From _G. C. Greubel_, Jul 14 2018: (Start)
%F a(n) = 4^n * Hermite(n, 5/8).
%F E.g.f.: exp(5*x - 16*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/4)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,5/8],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011 *)
%t Table[4^n*HermiteH[n, 5/8], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,5/8)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(5*x - 16*x^2))) \\ _G. C. Greubel_, Jul 14 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/4)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018
%Y Cf. A159014, A159017.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009