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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

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]]

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 June 19 12:57 EDT 2019. Contains 324222 sequences. (Running on oeis4.)