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%I #13 Mar 05 2018 11:06:45
%S 1,-462,-24948,-2518824,-654112074,-212483064024,-76819071738024,
%T -29728723632736128,-12066341379893331300,-5073593348593538950566,
%U -2192302482140061697816872,-968086916154014421082349304,-435126775136273350146250044888
%N Coefficients in expansion of E_6^(11/12).
%C In general, for 0 < m < 1, the expansion of (E_6)^m is asymptotic to -m * Gamma(1/4)^(16*m) * 3^(2*m) * exp(2*Pi*n) / (2^(13*m) * Pi^(12*m) * Gamma(1-m) * n^(1+m)). - _Vaclav Kotesovec_, Mar 05 2018
%F G.f.: Product_{n>=1} (1-q^n)^(11*A288851(n)/12).
%F a(n) ~ c * exp(2*Pi*n) / n^(23/12), where c = -11 * 2^(5/12) * 3^(5/6) * Pi^(11/3) / (128 * Gamma(1/12) * Gamma(3/4)^(44/3)) = -0.08406022472181281739983743854923746657261382508944840919197295490535... - _Vaclav Kotesovec_, Jul 08 2017
%t nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(11/12), {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), A289347 (k=9), A289348 (k=10), this sequence (k=11).
%Y Cf. A013973 (E_6), A288851.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jul 03 2017