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Coefficients of (q*(j(q)-1728))^(1/6) where j(q) is the elliptic modular invariant.
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%I #11 Mar 07 2018 17:16:38

%S 1,-164,-34426,-9943880,-3522075375,-1378091288700,-572783373894746,

%T -247966590624315128,-110550043138808626860,-50393645499572805001180,

%U -23374903983625804137812564,-10995211137216964385513242408

%N Coefficients of (q*(j(q)-1728))^(1/6) where j(q) is the elliptic modular invariant.

%F G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/6).

%F a(n) ~ c * exp(2*Pi*n) / n^(4/3), where c = -2^(1/3) * Pi^(1/3) * exp(-Pi/3) / (3^(1/3) * Gamma(2/3) * Gamma(3/4)^(4/3)) = -0.252847812633789641246665071437... - _Vaclav Kotesovec_, Mar 07 2018

%t CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(1/6), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 07 2018 *)

%Y (q*(j(q)-1728))^(k/24): A106203 (k=1), A289330 (k=2), A289331 (k=3), this sequence (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