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Numerator of Hermite(n, 8/13).
1

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

%S 1,16,-82,-12128,-110900,14622656,421383496,-22912610432,

%T -1363595118448,40138176712960,4790267177726176,-59022762446185984,

%U -18754577565924898112,-60676916573068018688,81436783159504914005120,1590111699775836488513536,-387442703422276530189741824

%N Numerator of Hermite(n, 8/13).

%H G. C. Greubel, <a href="/A159501/b159501.txt">Table of n, a(n) for n = 0..422</a>

%F From _G. C. Greubel_, Jun 12 2018: (Start)

%F a(n) = 13^n * Hermite(n,8/13).

%F E.g.f.: exp(16*x-169*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/13)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,8/13],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 14 2011 *)

%o (PARI) a(n)=numerator(polhermite(n,8/13)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 12 2018

%Y Cf. A159280, A159488.

%K sign,frac

%O 0,2

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