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Numerator of Hermite(n, 17/18).
2

%I #12 Sep 08 2022 08:45:44

%S 1,17,127,-3349,-118655,153017,98711839,1529368739,-85939956863,

%T -3443041152415,66768757515199,6712795544670683,-4864401632683007,

%U -13132369366595418871,-213005849393691708065,26163114283745650962323,962377156850346916957441

%N Numerator of Hermite(n, 17/18).

%H G. C. Greubel, <a href="/A159563/b159563.txt">Table of n, a(n) for n = 0..450</a>

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

%F a(n) = 9^n * Hermite(n, 17/18).

%F E.g.f.: exp(17*x - 81*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,17/18],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 20 2011 *)

%t Table[9^n*HermiteH[n, 17/18], {n,0,50}] (* _G. C. Greubel_, Jul 10 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,17/18)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(17/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 10 2018

%Y Cf. A159545, A159546.

%K sign,frac

%O 0,2

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