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G.f.: Sum_{k>=1} x^k/(1-x^k) * Product_{k>=1} 1/(1-x^k)^2.
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%I #7 May 26 2018 18:24:22

%S 0,1,4,11,27,58,119,227,420,744,1287,2160,3561,5739,9113,14224,21924,

%T 33327,50126,74531,109802,160211,231875,332821,474313,671072,943411,

%U 1317826,1830290,2527583,3472446,4746093,6456291,8741999,11785768,15822047,21156278

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

%C Convolution of A006128 and A000041.

%H Vaclav Kotesovec, <a href="/A305119/b305119.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(2*Pi*sqrt(n/3)) * (2*gamma + log(3*n/Pi^2)) / (8*3^(1/4)*Pi*n^(3/4)), 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)^2, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000041, A000712, A006128, A305082, A305102, A305120.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, May 26 2018