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%I #13 Sep 08 2022 08:45:45
%S 1,24,-1106,-107280,3006156,793927584,-6227509944,-8161777416384,
%T -122559955912560,106883437972961664,4420515123955413216,
%U -1691687063730285271296,-122388860352949901833536,31207679045861280271833600,3425139117578273280016104576
%N Numerator of Hermite(n, 12/29).
%H G. C. Greubel, <a href="/A160260/b160260.txt">Table of n, a(n) for n = 0..372</a>
%F From _G. C. Greubel_, Sep 26 2018: (Start)
%F a(n) = 29^n * Hermite(n, 12/29).
%F E.g.f.: exp(24*x - 841*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 24/29, -1106/841, -107280/24389, 3006156/707281,...
%t Table[29^n*HermiteH[n, 12/29], {n, 0, 30}] (* _G. C. Greubel_, Sep 26 2018 *)
%t HermiteH[Range[0,20],12/29]//Numerator (* _Harvey P. Dale_, Dec 27 2019 *)
%o (PARI) a(n)=numerator(polhermite(n, 12/29)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 841*x^2))) \\ _G. C. Greubel_, Sep 26 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 26 2018
%Y Cf. A009973 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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