A159030 - OEIS

%I #16 Sep 08 2022 08:45:43

%S 1,2,-158,-964,74860,774392,-59087816,-870884656,65263814032,

%T 1259194142240,-92636252574176,-2225167015577152,160627468056027328,

%U 4646979614394038144,-328987488497205476480,-11197324742440089463552,777044947563329128919296

%N Numerator of Hermite(n, 1/9).

%H G. C. Greubel, <a href="/A159030/b159030.txt">Table of n, a(n) for n = 0..450</a>

%F From _G. C. Greubel_, Jun 09 2018: (Start)

%F a(n) = 9^n * Hermite(n, 1/9).

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

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

%t Numerator[Table[HermiteH[n,1/9],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*)

%o (PARI) a(n)=numerator(polhermite(n,1/9)) \\ _Charles R Greathouse IV_, Jan 29 2016

%o (PARI) for(n=0,30, print1(9^n*polhermite(n,1/9), ", ")) \\ _G. C. Greubel_, Jun 10 2018

%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/9)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018

%Y Cf. A158811, A158954, A158960, A158980.

%K sign,frac

%O 0,2

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