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 A291695 Expansion of the series reversion of Sum_{i>=1} x^i/(1 - x^i) / Product_{j>=1} (1 - x^j). 0
 1, -3, 12, -57, 304, -1757, 10746, -68450, 449274, -3016645, 20618317, -142946735, 1002722249, -7103064540, 50738237140, -365049115546, 2642981328372, -19241453032254, 140770867457795, -1034409857616986, 7631075823632553, -56497364856268721, 419641611512419630, -3126180409889288924 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Reversion of g.f. for A006128. LINKS N. J. A. Sloane, Transforms Eric Weisstein's World of Mathematics, Series Reversion FORMULA G.f. A(x) satisfies: Sum_{i>=1} A(x)^i/(1 - A(x)^i) / Product_{j>=1} (1 - A(x)^j) = x. G.f. A(x) satisfies: Sum_{i>=1} i*A(x)^i / Product_{j=1..i} (1 - A(x)^j) = x. MATHEMATICA 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]] 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 *) CROSSREFS Cf. A006128, A007312, A050393, A176025. Sequence in context: A151498 A103370 A094149 * A117107 A159609 A128326 Adjacent sequences:  A291692 A291693 A291694 * A291696 A291697 A291698 KEYWORD sign AUTHOR Ilya Gutkovskiy, Aug 30 2017 STATUS approved

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Last modified April 20 11:36 EDT 2021. Contains 343135 sequences. (Running on oeis4.)