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%I #11 Sep 08 2022 08:45:44
%S 1,10,-1358,-42740,5512492,304384600,-37142220680,-3034178687600,
%T 348731717384080,38877977386007200,-4187277821653825760,
%U -608713688504523233600,61068424818638825202880,11260738942261526747094400,-1044883534589865025424443520
%N Numerator of Hermite(n, 5/27).
%H G. C. Greubel, <a href="/A160104/b160104.txt">Table of n, a(n) for n = 0..376</a>
%F From _G. C. Greubel_, Jul 12 2018: (Start)
%F a(n) = 27^n * Hermite(n, 5/27).
%F E.g.f.: exp(10*x - 729*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/27)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 10/27, -1358/729, -42740/19683, 5512492/531441..
%t Numerator[Table[HermiteH[n, 5/27], {n, 0, 30}]] (* or *) Table[27^n* HermiteH[n, 5/27], {n,0,30}] (* _G. C. Greubel_, Jul 12 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,5/27)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 12 2018
%Y Cf. A009971 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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