A291489 Expansion of the series reversion of -1 + Product_{k>=1} (1 + x^k)^k.

1, -2, 3, 2, -41, 196, -541, 229, 7235, -48228, 175956, -254933, -1575661, 14909191, -67194669, 153944915, 292516673, -4968647665, 27275432639, -82747735226, 3883854725, 1660136515050, -11302429310683, 42362000190568, -53376259124482, -520085199830413, 4671353423344131

Offset: 1

Author

Ilya Gutkovskiy, Aug 24 2017

Keywords

• sign

Comments

Reversion of g.f. (with constant term omitted) for A026007.

Links

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

Crossrefs

Cf. A007312, A026007, A050393, A176025.

Programs

Mathematica

nmax = 27; Rest[CoefficientList[InverseSeries[Series[-1 + Product[(1 + x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x], x]]
nmax = 27; Rest[CoefficientList[InverseSeries[Series[-1 + Exp[Sum[(-1)^(k + 1) x^k/(k (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)^k = x.