A291646 Expansion of the series reversion of -1 + Product_{k>=1} (1 + x^(2*k-1)).

1, 0, -1, -1, 2, 6, -1, -29, -32, 108, 311, -185, -1991, -1590, 9468, 22163, -26645, -170511, -70359, 955734, 1755790, -3561052, -16020532, 309754, 102695477, 141637053, -463468990, -1567907433, 806541136, 11367276801, 10768399120, -59447130815, -155142592628, 172852194214, 1273466836673

Offset: 1

Author

Ilya Gutkovskiy, Aug 28 2017

Keywords

• sign

Comments

Reversion of g.f. (with constant term omitted) for A000700.

Links

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

Crossrefs

Cf. A000700, A007312, A050393, A291489.

Programs

Mathematica

nmax = 35; Rest[CoefficientList[InverseSeries[Series[-1 + Product[1 + x^(2 k - 1), {k, 1, nmax}], {x, 0, nmax}], x], x]]
nmax = 35; Rest[CoefficientList[InverseSeries[Series[-1 + QPochhammer[x^2]^2/(QPochhammer[x] QPochhammer[x^4]), {x, 0, nmax}], x], x]]

Formula

G.f. A(x) satisfies: -1 + Product_{k>=1} (1 + A(x)^(2*k-1)) = x.