A292406 Expansion of Product_{k>=1} ((1 + k^k*x^k)/(1 - k^k*x^k)).

1, 2, 10, 72, 670, 7896, 113572, 1939028, 38463550, 869985586, 22098989952, 622728621984, 19271496576612, 649553583740576, 23680212403186584, 928276782505698920, 38931911577966732814, 1739307919812511213916, 82457732209611432170734

Offset: 0

Author

Seiichi Manyama, Sep 15 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A023882, A265949, A292407.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 + k^k*x^k)/(1 - k^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 16 2017 *)

Formula

Convolution of A023882 and A265949.

a(n) ~ 2*n^n * (1 + 2*exp(-1)/n + (exp(-1) + 10*exp(-2))/n^2). - Vaclav Kotesovec, Sep 16 2017