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%I #13 Sep 08 2022 08:45:44
%S 1,8,-1394,-34480,5821516,247659488,-40457575736,-2490185806912,
%T 392988531506320,32189435503872128,-4899280026394954016,
%U -508516209857615258368,74506523384461350441664,9493051794744527363939840,-1336252229871124217359780736
%N Numerator of Hermite(n, 4/27).
%H G. C. Greubel, <a href="/A160103/b160103.txt">Table of n, a(n) for n = 0..375</a>
%F From _G. C. Greubel_, Sep 24 2018: (Start)
%F a(n) = 27^n * Hermite(n, 4/27).
%F E.g.f.: exp(8*x - 729*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 8/27, -1394/729, -34480/19683, 5821516/531441, ...
%t Table[27^n*HermiteH[n, 4/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 4/27)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018
%Y Cf. A009971 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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