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A160251 Numerator of Hermite(n, 8/29). 1

%I

%S 1,16,-1426,-76640,5969356,611143616,-40423986104,-6814445150336,

%T 366920889983120,97565908182651136,-3993393901642052384,

%U -1704952878058464945664,46606527919245814078144,35158473337439989488532480,-456562766083189138816177024

%N Numerator of Hermite(n, 8/29).

%H Vincenzo Librandi, <a href="/A160251/b160251.txt">Table of n, a(n) for n = 0..200</a>

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

%F a(n) = 29^n * Hermite(n, 8/29).

%F E.g.f.: exp(16*x - 841*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

%e Numerators of 1, 16/29, -1426/841, -76640/24389, 5969356/707281, ...

%t Numerator[HermiteH[Range[0,20],8/29]] (* _Harvey P. Dale_, Jul 22 2014 *)

%t Table[29^n*HermiteH[n, 8/29], {n,0,30}] (* _G. C. Greubel_, Jul 12 2018 *)

%t a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Exp[ 16 x - 841 x^2], {x, 0, n}]]; (* _Michael Somos_, Jul 30 2018 *)

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

%o (MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(16/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 12 2018

%o (GAP) List(List([0..15],n->Sum([0..Int(n/2)],k->(-1)^k*Factorial(n)*(16/29)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))),NumeratorRat); # _Muniru A Asiru_, Jul 12 2018

%Y Cf. A009973 (denominators).

%K sign,frac

%O 0,2

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

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Last modified April 12 11:46 EDT 2021. Contains 342920 sequences. (Running on oeis4.)