A299831 Coefficients in expansion of (q*j(q))^(-1/3) where j(q) is the elliptic modular invariant (A000521).

1, -248, 57380, -13242240, 3055845770, -705181025216, 162730809182936, -37552508189222400, 8665789092645124915, -1999757252424845206240, 461473159094045987499908, -106491663578673234478298880, 24574504905153510156698896190

Offset: 0

Author

Seiichi Manyama, Feb 20 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..422

Crossrefs

Cf. A000521, A007245.

Programs

Mathematica

CoefficientList[Series[(2 * QPochhammer[-1, x])^8 / (65536 + x*QPochhammer[-1, x]^24), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 20 2018 *)

Formula

Convolution inverse of A007245.

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n), where c = 1.077593073040317872038995220477192961256589630965039133409... = 2 * exp(Pi/sqrt(3)) * Pi^4 / (3 * Gamma(1/3)^6). - Vaclav Kotesovec, Feb 20 2018, updated Mar 06 2018