A294954 Expansion of Product_{k>=1} 1/(1 - k^(2*k)*x^k)^k.

1, 1, 33, 2220, 265132, 49163241, 13121450895, 4762820449382, 2257130616816421, 1353302193751862072, 1001440612663683369940, 896481723303781965832069, 954894526385647926192875010, 1193519555165192704579377833814

Offset: 0

Author

Seiichi Manyama, Nov 12 2017

Keywords

• nonn

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n, g(n) = n^(2*n).

Links

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

Crossrefs

Column k=2 of A294950.

Cf. A294953, A294955.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1 - k^(2*k)*x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 15 2017 *)

PARI

N=20; x='x+O('x^N); Vec(1/prod(k=1, N, (1-k^(2*k)*x^k)^k))

Formula

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} A294955(k)*a(n-k) for n > 0.

a(n) ~ n^(2*n+1). - Vaclav Kotesovec, Nov 15 2017