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Coefficients of (q*(j(q)-1728))^(5/24) where j(q) is the elliptic modular invariant.
13

%I #11 Mar 07 2018 17:17:15

%S 1,-205,-38830,-10493215,-3586921610,-1369515719416,-558606292282075,

%T -238153389340570570,-104811899537297598195,-47246821512435762941195,

%U -21700419062680514765163503,-10118052721530705778119535745

%N Coefficients of (q*(j(q)-1728))^(5/24) where j(q) is the elliptic modular invariant.

%F G.f.: Product_{k>=1} (1-q^k)^(5*A289061(k)/24).

%F a(n) ~ c * exp(2*Pi*n) / n^(17/12), where c = -5 * 3^(1/3) * Gamma(2/3)^2 * exp(-5*Pi/12) * Gamma(1/12) / (2^(49/12) * Pi^(19/12) * Gamma(3/4)^(5/3)) = -0.28184482434015938133067183460309604452260645657140372869996481157015... - _Vaclav Kotesovec_, Mar 07 2018

%t CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(5/24), {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), A289332 (k=4), this sequence (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