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%I #9 Mar 24 2023 14:56:46
%S 1,-3,14,-82,541,-3833,28479,-218927,1726651,-13893013,113594944,
%T -941109972,7883133111,-66651214993,568062130934,-4875322862342,
%U 42097583306171,-365467693020273,3188024056471074,-27929166139563662,245625484632281831,-2167751159576883103,19192382951736683739
%N Expansion of the series reversion of x*(1 + 2*x)/(1 - x - x^2).
%C Reversion of g.f. for the Lucas numbers (beginning with 1) (A000204).
%H Vaclav Kotesovec, <a href="/A291535/b291535.txt">Table of n, a(n) for n = 1..500</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SeriesReversion.html">Series Reversion</a>
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F G.f. A(x) satisfies: A(x)*(1 + 2*A(x))/(1 - A(x) - A(x)^2) = x.
%F a(n) ~ -(-1)^n * 5^((n+1)/2) * phi^(3*n - 9/2) / (2*sqrt(Pi)*n^(3/2)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Nov 11 2017
%F D-finite with recurrence 2*n*a(n) +3*(7*n-10)*a(n-1) +5*(4*n-9)*a(n-2) +5*(n-3)*a(n-3)=0. - _R. J. Mathar_, Mar 24 2023
%t Rest[CoefficientList[InverseSeries[Series[x (1 + 2 x)/(1 - x - x^2), {x, 0, 23}], x], x]]
%Y Cf. A000204, A007440.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, Aug 25 2017
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