A159537 - OEIS

%I #12 Sep 08 2022 08:45:43

%S 1,18,-254,-25380,-16404,58383288,1098306744,-182703721392,

%T -7732416071280,705638518433568,52925521734602784,

%U -3125931245323172928,-392767229604421613376,14611648984681938387840,3214262644971898893888384,-60380735974552065344410368

%N Numerator of Hermite(n, 9/17).

%H G. C. Greubel, <a href="/A159537/b159537.txt">Table of n, a(n) for n = 0..404</a>

%F From _G. C. Greubel_, Jul 02 2018: (Start)

%F a(n) = 17^n * Hermite(n, 9/17).

%F E.g.f.: exp(18*x-289*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/17)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,9/17],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 08 2011 *)

%t Table[17^n*HermiteH[n, 9/17], {n,0,50}] (* _G. C. Greubel_, Jul 02 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,9/17)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/17)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 02 2018

%Y Cf. A159534, A159535, A159536.

%K sign,frac

%O 0,2

%A _N. J. A. Sloane_, Nov 12 2009