A299829 Coefficients in expansion of (q*j(q))^(-5/24) where j(q) is the elliptic modular invariant (A000521).

1, -155, 28655, -5760440, 1202381535, -256382973906, 55428428962345, -12099932165757725, 2660417880657190215, -588191792902675685120, 130616050711284314803809, -29108986917589590736384395, 6506478780288042396481955095

Offset: 0

Author

Seiichi Manyama, Feb 20 2018

Keywords

• sign

Crossrefs

Cf. A000521, A289300.

Programs

Mathematica

CoefficientList[Series[(2 * QPochhammer[-1, x])^5 / (65536 + x*QPochhammer[-1, x]^24)^(15/24), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 20 2018 *)

Formula

Convolution inverse of A289300.

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(3/8), where c = 0.730428963078390701326735403005831754545040392327211512089... = 2^(5/8) * exp(5 * Pi / (8 * sqrt(3))) * Pi^(5/2) / (3^(5/8) * Gamma(1/3)^(15/4) * Gamma(5/8)). - Vaclav Kotesovec, Feb 20 2018, updated Mar 06 2018

a(n) * A289300(n) ~ -5*sqrt(2 + sqrt(2)) * exp(2*sqrt(3)*Pi*n) / (16*Pi*n^2). - Vaclav Kotesovec, Feb 20 2018