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A277465 Expansion of e.g.f. log(1+x)/(1 + LambertW(-x)).

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%I A277465 #16 Apr 25 2023 14:36:22
%S A277465 0,1,1,11,86,1084,15654,275113,5548024,127423728,3272008650,
%T A277465 92988690893,2896148079516,98104636748468,3590611928294286,
%U A277465 141201205469361945,5937400341113630032,265833516437952849024,12625912572901413474834,634047172218326393377149
%N A277465 Expansion of e.g.f. log(1+x)/(1 + LambertW(-x)).
%H A277465 Robert Israel, <a href="/A277465/b277465.txt">Table of n, a(n) for n = 0..386</a>
%F A277465 E.g.f.: log(1+x)/(1 + LambertW(-x)).
%F A277465 a(n) ~ log(1+exp(-1)) * n^n.
%F A277465 a(n) = (-1)^(n+1)*(n-1)! + Sum_{j=1..n-1} a(j)*binomial(n,j)*(n-j)^(n-j-1). - _Robert Israel_, Oct 26 2016
%p A277465 S:= series(log(1+x)/(1+LambertW(-x)), x, 51):
%p A277465 seq(coeff(S,x,n)*n!, n=0..50); # _Robert Israel_, Oct 26 2016
%t A277465 CoefficientList[Series[Log[1+x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!
%o A277465 (PARI) x='x+O('x^50); concat([0],Vec(serlaplace(log(1+x)/(1 + lambertw(-x))))) \\ _G. C. Greubel_, Nov 07 2017
%Y A277465 Cf. A000312, A086331, A277466.
%K A277465 nonn
%O A277465 0,4
%A A277465 _Vaclav Kotesovec_, Oct 16 2016