A305120 - OEIS

%I #6 May 26 2018 18:24:06

%S 0,0,1,6,21,60,148,334,702,1396,2660,4880,8687,15044,25470,42212,

%T 68724,110000,173522,269930,414812,630032,947007,1409266,2078335,

%U 3038540,4407334,6344176,9068278,12874676,18164356,25472626,35519617,49259628,67964527,93308202

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

%C Self-convolution of A006128.

%H Vaclav Kotesovec, <a href="/A305120/b305120.txt">Table of n, a(n) for n = 0..10000</a>

%F 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.

%t 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]

%Y Cf. A006128, A000712, A305119.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, May 26 2018