A289330 Coefficients of (q*(j(q)-1728))^(1/12) where j(q) is the elliptic modular invariant.

1, -82, -20575, -6659090, -2518748380, -1032593788260, -445059365317243, -198496352611395190, -90757000595281589335, -42287493553947286567980, -19998274348368716713055507, -9571416182750599673509425808

Offset: 0

Author

Seiichi Manyama, Jul 02 2017

Keywords

• sign

Crossrefs

(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).

Cf. A289061.

Programs

Mathematica

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 *)

Formula

G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/12).

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