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%I #4 Aug 28 2017 20:17:41
%S 1,0,-1,-1,2,6,-1,-29,-32,108,311,-185,-1991,-1590,9468,22163,-26645,
%T -170511,-70359,955734,1755790,-3561052,-16020532,309754,102695477,
%U 141637053,-463468990,-1567907433,806541136,11367276801,10768399120,-59447130815,-155142592628,172852194214,1273466836673
%N Expansion of the series reversion of -1 + Product_{k>=1} (1 + x^(2*k-1)).
%C Reversion of g.f. (with constant term omitted) for A000700.
%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: -1 + Product_{k>=1} (1 + A(x)^(2*k-1)) = x.
%t nmax = 35; Rest[CoefficientList[InverseSeries[Series[-1 + Product[1 + x^(2 k - 1), {k, 1, nmax}], {x, 0, nmax}], x], x]]
%t nmax = 35; Rest[CoefficientList[InverseSeries[Series[-1 + QPochhammer[x^2]^2/(QPochhammer[x] QPochhammer[x^4]), {x, 0, nmax}], x], x]]
%Y Cf. A000700, A007312, A050393, A291489.
%K sign
%O 1,5
%A _Ilya Gutkovskiy_, Aug 28 2017