A291488 Expansion of the series reversion of -1 + Product_{k>=1} 1/(1 - x^k)^k.

1, -3, 12, -58, 318, -1896, 11966, -78595, 531486, -3674324, 25845131, -184348434, 1330147092, -9690872427, 71189146313, -526703176813, 3921274277132, -29354616797397, 220824254874928, -1668453804382315, 12655766723174710, -96340024533522759, 735747052686408916, -5635489764030599334

Offset: 1

Author

Ilya Gutkovskiy, Aug 24 2017

Keywords

• sign

Comments

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

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Series Reversion
• Index entries for reversions of series

Crossrefs

Cf. A000219, A007312, A050393, A176025.

Programs

Mathematica

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

Formula

G.f. A(x) satisfies: -1 + Product_{k>=1} 1/(1 - A(x)^k)^k = x.