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%I #12 Mar 07 2018 17:15:21
%S 1,-82,-20575,-6659090,-2518748380,-1032593788260,-445059365317243,
%T -198496352611395190,-90757000595281589335,-42287493553947286567980,
%U -19998274348368716713055507,-9571416182750599673509425808
%N Coefficients of (q*(j(q)-1728))^(1/12) where j(q) is the elliptic modular invariant.
%F G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/12).
%F a(n) ~ c * exp(2*Pi*n) / n^(7/6), where c = -Pi^(2/3) * exp(-Pi/6) / (2^(1/6) * 3^(7/6) * Gamma(2/3)^2 * Gamma(3/4)^(2/3)) = -0.149642588746726354370104662... - _Vaclav Kotesovec_, Mar 07 2018
%t CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(1/12), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 07 2018 *)
%Y (q*(j(q)-1728))^(k/24): A106203 (k=1), this sequence (k=2), A289331 (k=3), A289332 (k=4), A289333 (k=5), A289334 (k=6), A007242 (k=12), A289063 (k=24).
%Y Cf. A289061.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jul 02 2017
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