A261566 Expansion of Product_{k>=1} (1/(1 + 2*x^k))^k.

1, -2, 0, -6, 16, -18, 48, -94, 208, -426, 752, -1646, 3360, -6578, 13056, -26358, 53456, -105890, 211392, -424366, 850544, -1699290, 3393136, -6795646, 13601184, -27188130, 54358000, -108752870, 217552976, -435033618, 869999584, -1740145118, 3480497584

Offset: 0

Author

Vaclav Kotesovec, Aug 24 2015

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A071109, A255528, A261567.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1/(1 + 2*x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[Exp[Sum[(-1)^k*2^k/k*x^k/(1-x^k)^2, {k, 1, nmax}]], {x, 0, nmax}], x]

Formula

a(n) ~ c * (-2)^n, where c = Product_{j>=1} 1/(1 - 1/(-2)^j)^(j+1) = 0.81033497534928929188778847125052151513524786804782471307090750707405...