%I #17 Sep 08 2022 08:45:44
%S 1,24,-482,-62352,33420,264675744,6175426056,-1531951397568,
%T -82502038912368,10986387695118720,1049257719206417376,
%U -91053796553402040576,-14396552453405934395712,810501742160249881655808,217462224255991218838362240,-6786058422733831994965134336
%N Numerator of Hermite(n, 12/23).
%H G. C. Greubel, <a href="/A159877/b159877.txt">Table of n, a(n) for n = 0..385</a>
%F From _G. C. Greubel_, Jul 16 2018: (Start)
%F a(n) = 23^n * Hermite(n, 12/23).
%F E.g.f.: exp(24*x - 529*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 24/23, -482/529, -62352/12167, 33420/279841, ...
%t HermiteH[Range[0,20],12/23]//Numerator (* _Harvey P. Dale_, Jan 09 2017 *)
%t Table[23^n*HermiteH[n, 12/23], {n,0,30}] (* _G. C. Greubel_, Jul 16 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 12/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 16 2018
%Y Cf. A009967 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009