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%I #8 Mar 31 2018 07:10:50
%S 1,1,5,12,36,80,215,476,1154,2539,5772,12417,27146,57111,120822,
%T 249389,514201,1041684,2103211,4189502,8306632,16296337,31803839,
%U 61530913,118413823,226200319,429857982,811633548,1524828119,2848379512,5295550209
%N Expansion of Product_{k>=1} 1/(1 - x^k)^A007437(k).
%C Euler transform of A007437.
%H Vaclav Kotesovec, <a href="/A301873/b301873.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(2^(7/4) * Pi * Zeta(3)^(1/4) * n^(3/4) / (3^(5/4) * 5^(1/4)) + sqrt(5*Zeta(3)*n/6)/2 - (7*Pi * 5^(1/4) / (2^(15/4) * 3^(7/4) * Zeta(3)^(1/4)) + 5^(5/4) * Zeta(3)^(3/4) / (2^(15/4) * 3^(3/4) * Pi)) * n^(1/4) + (17*Zeta(3))/(72*Pi^2) + 23/576) * A^(1/4) * Zeta(3)^(23/192) / (2^(307/192) * 15^(23/192) * n^(119/192)), where A is the Glaisher-Kinkelin constant A074962.
%t nmax = 40; CoefficientList[Series[Exp[Sum[Sum[(DivisorSigma[1, k] + DivisorSigma[2, k]) * x^(j*k) / (2*j), {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 31 2018 *)
%Y Cf. A007437, A301874.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 28 2018