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%I #8 Oct 16 2017 19:55:41
%S 1,0,-1,0,2,-1,-5,7,13,-37,-27,175,-2,-768,521,3120,-4457,-11394,
%T 28363,34269,-157108,-56124,790091,-270661,-3638871,3821242,15153860,
%U -29235087,-54470264,182441139,143800906,-1008933847,-16080652,5067562024,-3456404771,-23114068193,33623924709,93441615451
%N Expansion of the series reversion of x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - x^5/(1 - ...))))), a continued fraction.
%C Reversion of 1 - 1/g(x) where g(x) = g.f. for A005169.
%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 - A(x)^2/(1 - A(x)^3/(1 - A(x)^4/(1 - A(x)^5/(1 - ...))))) = x.
%t nmax = 38; Rest[CoefficientList[InverseSeries[Series[x/(1 + ContinuedFractionK[-x^k, 1, {k, 2, nmax}]), {x, 0, nmax}], x], x]]
%t nmax = 38; Rest[CoefficientList[InverseSeries[Series[1 - Sum[(-1)^i x^(i^2)/Product[(1 - x^j), {j, 1, i}], {i, 0, nmax}]/Sum[(-1)^i x^(i (i + 1))/Product[(1 - x^j), {j, 1, i}], {i, 0, nmax}], {x, 0, nmax}], x], x]]
%Y Cf. A005169, A291148, A291377.
%K sign
%O 1,5
%A _Ilya Gutkovskiy_, Oct 15 2017
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