A294608 -id:A294608 - cp's OEIS frontend

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

Seiichi Manyama, Nov 04 2017

sign

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

Column k=1 of A294605.

Cf. A294608.

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

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

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

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Nov 04 2017

nonn

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

Column k=1 of A294609.

Cf. A294606, A294608.

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

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

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

cp's OEIS Frontend

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

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