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Coefficients in expansion of E_6^(3/4).
11

%I #14 Mar 05 2018 09:33:55

%S 1,-378,-36288,-6664896,-1950813774,-672039262944,-253536117254784,

%T -101485291597998336,-42360328701954544176,-18242860786892766495450,

%U -8049299329628263783504512,-3621056234759774113947852096

%N Coefficients in expansion of E_6^(3/4).

%F G.f.: Product_{n>=1} (1-q^n)^(3*A288851(n)/4).

%F a(n) ~ c * exp(2*Pi*n) / n^(7/4), where c = -3^(5/2) * Gamma(1/4)^11 / (2048 * 2^(3/4) * Pi^9) = -0.21604472104032272720247495618663130188448925463945370445... - _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}])^(3/4), {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), A289346 (k=8), this sequence (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