%I #14 Mar 05 2018 09:33:07

%S 1,-336,-39312,-8266944,-2529479568,-895678457184,-344891780549568,

%T -140330667583849344,-59379605532142099344,-25873741825665005773200,

%U -11534062764689844375098592,-5236325710480558290644292672

%N Coefficients in expansion of E_6^(2/3).

%F G.f.: Product_{n>=1} (1-q^n)^(2*A288851(n)/3).

%F a(n) ~ c * exp(2*Pi*n) / n^(5/3), where c = -3^(1/3) * Gamma(1/4)^(32/3) / (128 * 2^(2/3) * Pi^8 * Gamma(1/3)) = -0.258650618394676269905172499217587002338... - _Vaclav Kotesovec_, Jul 08 2017, updated Mar 05 2018

%t nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(2/3), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 08 2017 *)

%Y E_6^(k/12): A109817 (k=1), A289325 (k=2), A289326 (k=3), A289327 (k=4), A289328 (k=5), A289293 (k=6), A289345 (k=7), this sequence (k=8), A289347 (k=9), A289348 (k=10), A289349 (k=11).

%Y Cf. A013973 (E_6), A288851.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jul 03 2017