A294606 Expansion of Product_{k>=1} (1 - k*x^k)^(k^k).

1, -1, -8, -73, -919, -13977, -253640, -5290184, -124681406, -3272865905, -94671665085, -2991846831531, -102566663464544, -3791541404744714, -150357943095635464, -6367699625807475503, -286854179220742344135, -13697182490105378305606

Offset: 0

Author

Seiichi Manyama, Nov 04 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..385

Crossrefs

Column k=1 of A294605.

Cf. A294608.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 - k*x^k)^(k^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 05 2017 *)

PARI

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

Formula

a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} A294608(k) * a(n-k) for n > 0.