%I #11 Sep 08 2022 08:45:43

%S 1,10,-478,-16340,665452,44432600,-1478830280,-168880559600,

%T 4294541716880,823849124759200,-14101714763617760,

%U -4902865088744353600,40630051579638182080,34412572771327218390400,38831520143870883754880,-278078223664141142377568000

%N Numerator of Hermite(n, 5/17).

%H G. C. Greubel, <a href="/A159533/b159533.txt">Table of n, a(n) for n = 0..404</a>

%F From _G. C. Greubel_, Jul 09 2018: (Start)

%F a(n) = 17^n * Hermite(n, 5/17).

%F E.g.f.: exp(10*x-289*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/17)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,5/17],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2011 *)

%t Table[17^n*HermiteH[n, 5/17], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,5/17)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/17)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 09 2018

%Y Cf. A159529, A159530.

%K sign,frac

%O 0,2

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