A294773 -id:A294773 - cp's OEIS frontend

A294704 Expansion of Product_{k>=1} (1 - k^k*x^k)^(k^k).

1, -1, -16, -713, -64711, -9688521, -2165724176, -675843638952, -280752881225790, -149800127712465769, -99844730464906330029, -81300082264515781043363, -79413710307214816810372248, -91652445696245266803423194130

Offset: 0

Seiichi Manyama, Nov 07 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..214

Column k=1 of A294699.

Cf. A294757, A294773.

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

N=20; x='x+O('x^N); Vec(prod(k=1, N, (1-k^k*x^k)^k^k))

a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} A294773(k)*a(n-k) for n > 0.

a(n) ~ -n^(2*n). - Vaclav Kotesovec, Nov 09 2017

A294757 Expansion of Product_{k>=1} 1/(1 - k^k*x^k)^(k^k).

Original entry on oeis.org

1, 1, 17, 746, 66442, 9843731, 2187951485, 680615166718, 282199710311343, 150389915850565698, 100155578811552469018, 81505577529171038120173, 79580089696277797740768316, 91814299717377746850767747558

Offset: 0

Seiichi Manyama, Nov 08 2017

nonn

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = g(n) = n^n.

Seiichi Manyama, Table of n, a(n) for n = 0..214

Column k=1 of A294756.

Cf. A294704, A294773.

N=20; x='x+O('x^N); Vec(1/prod(k=1, N, (1-k^k*x^k)^k^k))

sd(n) = sumdiv(n, d, d^(d+n+1));
a(n) = if (n==0, 1, sum(k=1, n, sd(k)*a(n-k))/n); \\ Michel Marcus, Nov 10 2017

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} A294773(k)*a(n-k) for n > 0.

a(n) ~ n^(2*n). - Vaclav Kotesovec, Nov 08 2017

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A294704 Expansion of Product_{k>=1} (1 - k^k*x^k)^(k^k).

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A294757 Expansion of Product_{k>=1} 1/(1 - k^k*x^k)^(k^k).

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