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%I #22 Sep 08 2022 08:45:43
%S 1,5,7,-145,-1103,4925,123895,87575,-15172895,-88475275,2015632615,
%T 26003712575,-269076694895,-6962185390675,28153019652055,
%U 1895235816710375,1874863777497025,-536453596325102875,-3255976297539604025,157531083721635311375,1901199312366721133425
%N Numerator of Hermite(n, 5/6).
%H G. C. Greubel, <a href="/A158969/b158969.txt">Table of n, a(n) for n = 0..450</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 From _G. C. Greubel_, Jul 14 2018: (Start)
%F a(n) = 3^n * Hermite(n, 5/6).
%F E.g.f.: exp(5*x - 9*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/3)^(n-2*k)/(k!*(n-2*k)!)). (End)
%F D-finite with recurrence a(n) -5*a(n-1) +18*(n-1)*a(n-2)=0. - [DLMF] _Georg Fischer_, Feb 06 2021
%t Numerator[Table[HermiteH[n,5/6],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)
%t Table[3^n*HermiteH[n, 5/6], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)
%o (PARI) a(n)=numerator(polhermite(n,5/6)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(5*x - 9*x^2))) \\ _G. C. Greubel_, Jul 14 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/3)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018
%Y Cf. A158968.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009
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