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%I #21 Sep 08 2022 08:45:44
%S 1,24,-146,-38160,-599604,95815584,4464144456,-307933642944,
%T -29952193511280,1059772077373824,220063883293269216,
%U -2370021199600548096,-1804627869905557267776,-22777205204394225722880,16391584262028099097996416,623630012494691211958785024
%N Numerator of Hermite(n, 12/19).
%H Vincenzo Librandi, <a href="/A159650/b159650.txt">Table of n, a(n) for n = 0..200</a>
%H DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F D-finite with recurrence a(n) - 24*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - _R. J. Mathar_, Feb 16 2014
%F From _G. C. Greubel_, Jul 11 2018: (Start)
%F a(n) = 19^n * Hermite(n, 12/19).
%F E.g.f.: exp(24*x - 361*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e Numerator of 1, 24/19, -146/361, -38160/6859, -599604/130321, 95815584/2476099, ...
%p A159650 := proc(n)
%p orthopoly[H](n,12/19) ;
%p numer(%) ;
%p end proc: # _R. J. Mathar_, Feb 16 2014
%t Numerator[Table[HermiteH[n, 12/19], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 16 2011 *)
%t Table[19^n*HermiteH[n, 12/19], {n,0,50}] (* _G. C. Greubel_, Jul 11 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,12/19)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 11 2018
%Y Cf. A001029 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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