The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #6 Jun 16 2026 10:06:08
%S 0,0,1,5,14,35,78,164,331,638,1203,2197,3937,6915,11945,20319,34102,
%T 56541,92680,150391,241688,385056,608403,954033,1485268,2296836,
%U 3529317,5390769,8187309,12367754,18587283,27798372,41381012,61326589,90499658,133005971,194712792,283976310
%N Expansion of g.f. (Sum_{j>=1} x^j/(1-x^j))^2 * Product_{k>=1} (1+x^k)^k.
%F a(n) ~ exp(3^(4/3) * zeta(3)^(1/3) * n^(2/3) / 2^(4/3)) * (log(2*n/(3*zeta(3))) + 3*gamma)^2 / (27 * 2^(1/12) * sqrt(Pi*zeta(3))), where gamma is the Euler-Mascheroni constant A001620.
%t nmax = 40; CoefficientList[Series[Sum[x^j/(1-x^j), {j, 1, nmax}]^2 * Product[(1+x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A397040, A397078, A397080, A397082.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Jun 16 2026