A159232 Numerator of Hermite(n, 4/9).

1, 8, -98, -3376, 20620, 2352608, 2118664, -2269785664, -20560850288, 2777155418240, 52194963065824, -4081432073022208, -125662880767476032, 6929000903815364096, 320078034126827436160, -13154349776838626280448, -883024421142899680112384

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Formula

From G. C. Greubel, Jun 28 2018: (Start)

a(n) = 9^n * Hermite(n, 4/9).

E.g.f.: exp(8*x-81*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(8/9)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 4/9], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)

Prog

(PARI) a(n)=numerator(polhermite(n, 4/9)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(8/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 28 2018

Crossrefs

Cf. A159030, A159197.

Sequence in context: A228794 A366035 A211869 * A297958 A298774 A298581

Adjacent sequences: A159229 A159230 A159231 * A159233 A159234 A159235

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved