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%I #14 Mar 07 2018 17:16:01
%S 1,-123,-28341,-8688812,-3182839959,-1275218435124,-539854235696065,
%T -237249494737728429,-107125917871853210346,-49374268015554366062883,
%U -23126111889684391337303994,-10973394463170114841113101133
%N Coefficients of (q*(j(q)-1728))^(1/8) where j(q) is the elliptic modular invariant.
%H Seiichi Manyama, <a href="/A289331/b289331.txt">Table of n, a(n) for n = 0..367</a>
%F G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/8).
%F a(n) ~ c * exp(2*Pi*n) / n^(5/4), where c = -3^(1/2) * Pi^(1/4) * exp(-Pi/4) / (2^(7/4) * Gamma(3/4)^2) = -0.20815359871514720517220474749202446933362532... - _Vaclav Kotesovec_, Mar 07 2018
%t CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(1/8), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 07 2018 *)
%Y (q*(j(q)-1728))^(k/24): A106203 (k=1), A289330 (k=2), this sequence (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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