A294813 Expansion of Product_{k>=1} 1/(1 - k^k*x^k)^k.

1, 1, 9, 90, 1162, 17435, 310193, 6286826, 144750451, 3717959194, 105725550762, 3293914191401, 111659484775650, 4089936343858976, 160992739588472076, 6776415674628574634, 303714862444753023205, 14439925495117621425535

Offset

0,3

Comments

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

Links

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

Formula

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} A294810(k)*a(n-k) for n > 0.

a(n) ~ n^(n+1). - Vaclav Kotesovec, Nov 10 2017

Prog

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

Crossrefs

Cf. A294809, A294810.

Sequence in context: A276961 A062815 A294610 * A218118 A160569 A157545

Adjacent sequences: A294810 A294811 A294812 * A294814 A294815 A294816

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2017

Status

approved