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Numerator of Hermite(n, 18/23).
1

%I #16 Sep 08 2022 08:45:44

%S 1,36,238,-67608,-3189300,171302256,23038278216,-258048705312,

%T -179911241858928,-4292680465160640,1558578348234929376,

%U 101525379857857028736,-14483821141875255043392,-1810383783782862018394368,134036659769169225204616320,31640724357081844323823566336

%N Numerator of Hermite(n, 18/23).

%H G. C. Greubel, <a href="/A159921/b159921.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, 18/23).

%F E.g.f.: exp(36*x - 529*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 36/23, 238/529, -67608/12167, -3189300/279841, ...

%t Numerator[Table[HermiteH[n, 18/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 18/23], {n,0,30}] (* _G. C. Greubel_, Jul 16 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 18/23)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - 529*x^2))) \\ _G. C. Greubel_, Jul 16 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/23)^(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