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

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

Offset: 0

Author

Seiichi Manyama, Nov 08 2017

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Column k=1 of A294756.

Cf. A294704, A294773.

Programs

PARI

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

PARI

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

Formula

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