A159531 - OEIS

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

%S 1,6,-542,-10188,878700,28826856,-2366481864,-114170427792,

%T 8889763054992,581262636440160,-42756971593427424,

%U -3616239868184689344,250151386181903425728,26583148042820425844352,-1720138627513899785854080,-225431665727586284647620864

%N Numerator of Hermite(n, 3/17).

%H G. C. Greubel, <a href="/A159531/b159531.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, 3/17).

%F E.g.f.: exp(6*x-289*x^2).

%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/17)^(n-2*k)/(k!*(n-2*k)!)). (End)

%t Numerator[Table[HermiteH[n,3/17],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2011 *)

%t Table[17^n*HermiteH[n, 3/17], {n,0,30}] (* _G. C. Greubel_, Jul 09 2018 *)

%o (PARI) a(n)=numerator(polhermite(n,3/17)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(6/17)^(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. A159521, A159529, A159530.

%K sign,frac

%O 0,2

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