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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..450
Programs
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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
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Mathematica
Numerator[Table[HermiteH[n,4/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*) -
PARI
a(n)=numerator(polhermite(n,4/9)) \\ Charles R Greathouse IV, Jan 29 2016
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)