A281356 G.f.: 1 + Sum_{n>=1} x^(3*n-2) / Product_{k=1..n} (1-x^k).

1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 9, 10, 13, 17, 21, 25, 33, 39, 49, 60, 73, 88, 110, 130, 158, 191, 230, 273, 331, 391, 468, 556, 660, 779, 927, 1087, 1284, 1510, 1775, 2075, 2438, 2842, 3323, 3872, 4510

Offset: 0

Author

N. J. A. Sloane, Jan 22 2017

Keywords

• nonn

Links

• Roland Bacher, P. De La Harpe, Conjugacy growth series of some infinitely generated groups, hal-01285685v2, 2016.

Crossrefs

Apart from leading term, essentially identical to A008483.

Programs

Mathematica

nmax = 50; CoefficientList[Series[1 + Sum[x^(3*k-2)/QPochhammer[x, x, k], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 13 2017 *)
Flatten[{1, Table[PartitionsP[n] - PartitionsP[n-1] - PartitionsP[n-2] + PartitionsP[n-3], {n, 3, 50}]}] (* Vaclav Kotesovec, Oct 13 2017 *)

Formula

a(n) ~ Pi^2 * exp(Pi*sqrt(2*n/3)) / (12*sqrt(3)*n^2). - Vaclav Kotesovec, Oct 13 2017