A397079 - OEIS

%I #6 Jun 16 2026 10:04:40

%S 0,0,1,5,14,33,67,127,226,382,628,993,1541,2327,3468,5054,7297,10350,

%T 14568,20210,27854,37940,51381,68891,91910,121575,160092,209282,

%U 272447,352434,454197,582065,743347,944657,1196586,1509043,1897428,2376287,2967707,3693102,4583742

%N Expansion of g.f. (Sum_{j>=1} x^j/(1-x^j))^2 * Product_{k>=1} 1/(1-x^k).

%F a(n) ~ sqrt(3) * exp(Pi*sqrt(2*n/3)) * (log(6*n/Pi^2) + 2*gamma)^2 / (8*Pi^2), where gamma is the Euler-Mascheroni constant A001620.

%t nmax = 50; CoefficientList[Series[Sum[x^j/(1-x^j), {j, 1, nmax}]^2 / Product[1-x^k, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A006128, A397077, A397078.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Jun 16 2026