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%I #11 Jun 12 2024 01:11:34
%S 1,2,22,278,4822,104342,2709622,82092278,2842418902,110720079062,
%T 4792059271222,228144844817078,11849163703935382,666694458859845782,
%U 40397145162583154422,2622634244645856386678,181615748103175019442262,13362823095925278064444502,1041037845089466806646007222
%N Expansion of e.g.f. exp(-x) / (2 - exp(3*x)).
%H G. C. Greubel, <a href="/A367979/b367979.txt">Table of n, a(n) for n = 0..360</a>
%F a(n) = Sum_{k>=0} (3*k-1)^n / 2^(k+1).
%F a(n) = (-1)^n + Sum_{k=1..n} binomial(n,k) * 3^k * a(n-k).
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * 3^k * A000670(k).
%t nmax = 18; CoefficientList[Series[Exp[-x]/(2 - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t a[n_] := a[n] = (-1)^n + Sum[Binomial[n, k] 3^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
%o (Magma)
%o R<x>:=PowerSeriesRing(Rationals(), 40);
%o Coefficients(R!(Laplace( Exp(-x)/(2-Exp(3*x)) ))); // _G. C. Greubel_, Jun 11 2024
%o (SageMath)
%o def A367979_list(prec):
%o P.<x> = PowerSeriesRing(QQ, prec)
%o return P( exp(-x)/(2-exp(3*x)) ).egf_to_ogf().list()
%o A367979_list(40) # _G. C. Greubel_, Jun 11 2024
%Y Cf. A000670, A052841, A151919, A328182, A346208, A367977, A367980, A367981, A367982, A367983.
%K nonn,changed
%O 0,2
%A _Ilya Gutkovskiy_, Dec 07 2023
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