|
%I #6 Apr 21 2020 05:57:26
%S 1,-3,12,-57,304,-1757,10746,-68450,449274,-3016645,20618317,
%T -142946735,1002722249,-7103064540,50738237140,-365049115546,
%U 2642981328372,-19241453032254,140770867457795,-1034409857616986,7631075823632553,-56497364856268721,419641611512419630,-3126180409889288924
%N Expansion of the series reversion of Sum_{i>=1} x^i/(1 - x^i) / Product_{j>=1} (1 - x^j).
%C Reversion of g.f. for A006128.
%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_{i>=1} A(x)^i/(1 - A(x)^i) / Product_{j>=1} (1 - A(x)^j) = x.
%F G.f. A(x) satisfies: Sum_{i>=1} i*A(x)^i / Product_{j=1..i} (1 - A(x)^j) = x.
%t nmax = 24; Rest[CoefficientList[InverseSeries[Series[Sum[x^i/(1 - x^i), {i, 1, nmax}] / Product[1 - x^j, {j, 1, nmax}], {x, 0, nmax}], x], x]]
%t nmax = 24; Rest[CoefficientList[InverseSeries[Series[(Log[1-x] + QPolyGamma[0, 1, x]) / (Log[x]*QPochhammer[x]), {x, 0, nmax}], x], x]] (* _Vaclav Kotesovec_, Apr 21 2020 *)
%Y Cf. A006128, A007312, A050393, A176025.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, Aug 30 2017
|
