A291695 Expansion of the series reversion of Sum_{i>=1} x^i/(1 - x^i) / Product_{j>=1} (1 - x^j).

1, -3, 12, -57, 304, -1757, 10746, -68450, 449274, -3016645, 20618317, -142946735, 1002722249, -7103064540, 50738237140, -365049115546, 2642981328372, -19241453032254, 140770867457795, -1034409857616986, 7631075823632553, -56497364856268721, 419641611512419630, -3126180409889288924

Offset

1,2

Comments

Reversion of g.f. for A006128.

Links

Table of n, a(n) for n=1..24.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Series Reversion

Index entries for reversions of series

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