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%I #15 Sep 08 2022 08:45:44
%S 1,1,-287,-863,247105,1241281,-354589919,-2499523487,712353753217,
%T 6471255867265,-1839949672471199,-20477166570194399,
%U 5808483395818564033,76577571062410406977,-21670384262882293332575,-330431150786521054263839,93285628864864986142460161
%N Numerator of Hermite(n, 1/24).
%H G. C. Greubel, <a href="/A159949/b159949.txt">Table of n, a(n) for n = 0..428</a>
%F From _G. C. Greubel_, Jul 16 2018: (Start)
%F a(n) = 12^n * Hermite(n, 1/24).
%F E.g.f.: exp(x - 144*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/12)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerators of 1, 1/12, -287/144, -863/1728, 247105/20736, ...
%t Numerator[HermiteH[Range[0,20],1/24]] (* _Harvey P. Dale_, Nov 05 2016 *)
%t Table[12^n*HermiteH[n, 1/12], {n, 0, 30}] (* _G. C. Greubel_, Jul 16 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 1/24)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(x - 144*x^2))) \\ _G. C. Greubel_, Jul 16 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/12)^(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. A001021 (denominators).
%K sign,frac
%O 0,3
%A _N. J. A. Sloane_, Nov 12 2009
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