A291488 - OEIS

%I #5 Feb 16 2025 08:33:50

%S 1,-3,12,-58,318,-1896,11966,-78595,531486,-3674324,25845131,

%T -184348434,1330147092,-9690872427,71189146313,-526703176813,

%U 3921274277132,-29354616797397,220824254874928,-1668453804382315,12655766723174710,-96340024533522759,735747052686408916,-5635489764030599334

%N Expansion of the series reversion of -1 + Product_{k>=1} 1/(1 - x^k)^k.

%C Reversion of g.f. (with constant term omitted) for A000219.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H Eric Weisstein's World of Mathematics, <a href="https://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/(1 - A(x)^k)^k = x.

%t nmax = 24; Rest[CoefficientList[InverseSeries[Series[-1 + Product[1/(1 - x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x], x]]

%t nmax = 24; Rest[CoefficientList[InverseSeries[Series[-1 + Exp[Sum[DivisorSigma[2, k] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x], x]]

%Y Cf. A000219, A007312, A050393, A176025.

%K sign,changed

%O 1,2

%A _Ilya Gutkovskiy_, Aug 24 2017