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%I #4 Aug 23 2017 23:42:38
%S 1,0,-1,0,3,-1,-12,9,55,-67,-267,468,1323,-3180,-6513,21267,30969,
%T -140581,-135995,919698,494361,-5954217,-829116,38113425,-9433359,
%U -240844482,154219912,1499076989,-1585801575,-9161079266,13958031252,54710928759,-113373461193,-317030478360,875491422246
%N Expansion of the series reversion of Sum_{k>=1} x^(k*(k+1)/2).
%C Reversion of g.f. (with constant term omitted) for A010054.
%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: Sum_{k>=1} A(x)^(k*(k+1)/2) = x.
%t nmax = 35; Rest[CoefficientList[InverseSeries[Series[Sum[x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x], x]]
%t nmax = 35; Rest[CoefficientList[InverseSeries[Series[(-2 x^(1/8) + EllipticTheta[2, 0, Sqrt[x]])/(2 x^(1/8)), {x, 0, nmax}], x], x]]
%Y Cf. A006195, A010054, A179848, A259938.
%K sign
%O 1,5
%A _Ilya Gutkovskiy_, Aug 23 2017