A159030 Numerator of Hermite(n, 1/9).
1, 2, -158, -964, 74860, 774392, -59087816, -870884656, 65263814032, 1259194142240, -92636252574176, -2225167015577152, 160627468056027328, 4646979614394038144, -328987488497205476480, -11197324742440089463552, 777044947563329128919296
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)*(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
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Mathematica
Numerator[Table[HermiteH[n,1/9],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*) -
PARI
a(n)=numerator(polhermite(n,1/9)) \\ Charles R Greathouse IV, Jan 29 2016
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PARI
for(n=0,30, print1(9^n*polhermite(n,1/9), ", ")) \\ G. C. Greubel, Jun 10 2018
Formula
From G. C. Greubel, Jun 09 2018: (Start)
a(n) = 9^n * Hermite(n, 1/9).
E.g.f.: exp(2*x-81*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/9)^(n-2k)/(k!*(n-2k)!)). (End)