A294610 Expansion of Product_{k>=1} 1/(1 - k*x^k)^(k^k).

1, 1, 9, 90, 1154, 17427, 309117, 6285102, 144603015, 3717580810, 105696353842, 3293810230381, 111651093529948, 4089889271054734, 160989247361249558, 6776381334102511286, 303712681809603918633, 14439887378431671417669

Offset: 0

Author

Seiichi Manyama, Nov 04 2017

Keywords

• nonn

Links

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

Crossrefs

Column k=1 of A294609.

Cf. A294606, A294608.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(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(1/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.