A327684 Expansion of Product_{k>0} (1 + x^k/(1 + x^k/(1 + x^k))).

1, 1, 0, 4, -4, 11, -13, 39, -73, 144, -256, 559, -1116, 2188, -4317, 8804, -17591, 34992, -69815, 140097, -280416, 560077, -1119327, 2240719, -4482527, 8961129, -17920037, 35847885, -71699202, 143384383, -286760131, 573549105, -1147115913, 2294173485, -4588309651, 9176739373

Offset: 0

Author

Seiichi Manyama, Sep 22 2019

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000009, A268498, A327683.

Programs

Mathematica

m = 35; CoefficientList[Series[Product[(1 + x^k/(1 + x^k/(1 + x^k))), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 06 2021 *)

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+3*x^k+x^(2*k))/(1+2*x^k)))

Formula

a(n) ~ -(-1)^n * c * 2^n, where c = 1/4 * Product_{k>=2} (1 + (-1/2)^k/(1 + (-1/2)^k/(1 + (-1/2)^k))) = 0.267077782295890034289082591596560646781284184591415208072736792505213482... - Vaclav Kotesovec, May 06 2021