A305120 G.f.: (Sum_{k>=1} x^k/(1-x^k) * Product_{k>=1} 1/(1-x^k) )^2.

0, 0, 1, 6, 21, 60, 148, 334, 702, 1396, 2660, 4880, 8687, 15044, 25470, 42212, 68724, 110000, 173522, 269930, 414812, 630032, 947007, 1409266, 2078335, 3038540, 4407334, 6344176, 9068278, 12874676, 18164356, 25472626, 35519617, 49259628, 67964527, 93308202

Offset: 0

Author

Vaclav Kotesovec, May 26 2018

Keywords

• nonn

Comments

Self-convolution of A006128.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006128, A000712, A305119.

Programs

Mathematica

nmax = 40; CoefficientList[Series[(Sum[x^k/(1-x^k), {k, 1, nmax}] * Product[1/(1-x^k), {k, 1, nmax}])^2, {x, 0, nmax}], x]

Formula

a(n) ~ 3^(1/4)*(2*gamma+log(3*n/Pi^2))^2 * exp(2*Pi*sqrt(n/3)) / (16*Pi^2*n^(1/4)), where gamma is the Euler-Mascheroni constant A001620.