A291645 Expansion of the series reversion of -1 + Product_{k>=1} (1 + x^(k^2)).

1, 0, 0, -1, -1, 0, 4, 9, 4, -23, -78, -78, 132, 694, 1088, -443, -6169, -13452, -4646, 52247, 155891, 143796, -391672, -1715015, -2481013, 2107735, 17836000, 35704800, 3037215, -172386166, -465009936, -338007604, 1487272659, 5624864403, 7125599375, -10208041482

Offset: 1

Author

Ilya Gutkovskiy, Aug 28 2017

Keywords

• sign

Comments

Reversion of g.f. (with constant term omitted) for A033461.

Links

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

Crossrefs

Cf. A007312, A033461, A050393, A291489.

Programs

Mathematica

nmax = 36; Rest[CoefficientList[InverseSeries[Series[-1 + Product[1 + x^k^2, {k, 1, nmax}], {x, 0, nmax}], x], x]]

Formula

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