A292407 Expansion of Product_{k>=1} ((1 - k^k*x^k)/(1 + k^k*x^k)).

1, -2, -6, -40, -386, -4952, -77116, -1406164, -29389570, -692122610, -18136684128, -523599632000, -16516245738140, -565284631133600, -20867650682241704, -826570263691236456, -34971594470460748146, -1574134630989710480092

Offset: 0

Author

Seiichi Manyama, Sep 15 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A292311, A292312, A292406.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 - k^k*x^k)/(1 + k^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 16 2017 *)

Formula

Convolution of A292311 and A292312.

Convolution inverse of A292406.

a(n) ~ -2*n^n * (1 - 2*exp(-1)/n - (exp(-1) + 6*exp(-2))/n^2). - Vaclav Kotesovec, Sep 16 2017