%I #12 Sep 08 2022 08:45:44
%S 1,18,-398,-33156,265260,100529208,851937144,-420157660464,
%T -11868528214128,2213197138985760,116959244837147424,
%U -13874016936408533568,-1178622627351978445632,98989275444707922811776,12844358938330412301313920,-769385135305160262357781248
%N Numerator of Hermite(n, 9/19).
%H G. C. Greubel, <a href="/A159647/b159647.txt">Table of n, a(n) for n = 0..397</a>
%F From _G. C. Greubel_, Jul 14 2018: (Start)
%F a(n) = 19^n * Hermite(n, 9/19).
%F E.g.f.: exp(18*x - 361*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,9/19],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 20 2011 *)
%t Table[19^n*HermiteH[n, 9/19], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)
%o (PARI) a(n)=numerator(polhermite(n, 9/19)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 361*x^2))) \\ _G. C. Greubel_, Jul 14 2018
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/19)^(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. A159564, A159618, A159646.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009