A299828 Coefficients in expansion of (q*j(q))^(-1/6) where j(q) is the elliptic modular invariant (A000521).

1, -124, 21002, -4016872, 809288755, -167876361244, 35484423032510, -7599636959859112, 1643483711343623769, -358082233874320665600, 78482787856608918842534, -17284562763499415545585456, 3821876235203430873578026310

Offset: 0

Author

Seiichi Manyama, Feb 20 2018

Keywords

• sign

Crossrefs

Cf. A000521, A289299.

Programs

Mathematica

CoefficientList[Series[(2 * QPochhammer[-1, x])^4 / (65536 + x*QPochhammer[-1, x]^24)^(1/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 20 2018 *)

Formula

Convolution inverse of A289299.

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / sqrt(n), where c = 0.585669299547026632252908661746743778408088234535945502931... = sqrt(2) * exp(Pi/(2 * sqrt(3))) * Pi^(3/2) / (sqrt(3) * Gamma(1/3)^3). - Vaclav Kotesovec, Feb 20 2018, updated Mar 06 2018

a(n) * A289299(n) ~ -exp(2*sqrt(3)*Pi*n) / (2*Pi*n^2). - Vaclav Kotesovec, Feb 20 2018