A159621 - OEIS

%I #14 Sep 08 2022 08:45:44

%S 1,8,-658,-16816,1290700,58890208,-4188305336,-288618823744,

%T 18858744578192,1817932282570880,-108000664008524576,

%U -13989476392229950208,745825462417862580928,127171427161623189249536,-5982946372961072670593920,-1333312356733375778299061248

%N Numerator of Hermite(n, 4/19).

%H G. C. Greubel, <a href="/A159621/b159621.txt">Table of n, a(n) for n = 0..397</a>

%F From _G. C. Greubel_, Jul 14 2018: (Start)

%F a(n) = 19^n * Hermite(n, 4/19).

%F E.g.f.: exp(8*x - 361*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,4/19],{n,0,30}]] (* _Vladimir Joseph Stephan Orlovsky_, May 20 2011 *)

%t Table[19^n*HermiteH[n, 4/19], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)

%o (PARI) a(n)=numerator(polhermite(n, 4/19)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) x='x+O('x^30); Vec(serlaplace(exp(8*x - 361*x^2))) \\ _G. C. Greubel_, Jul 14 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018

%Y Cf. A159564, A159618.

%K sign,frac

%O 0,2

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