A299827 Coefficients in expansion of (q*j(q))^(-1/8) where j(q) is the elliptic modular invariant (A000521).

1, -93, 14310, -2598835, 504870840, -101820075030, 21033065244233, -4418043012449640, 939524696045366400, -201695299876429277490, 43625340820210623183729, -9493467131549164702157730, 2076344691467486382060290550

Offset: 0

Author

Seiichi Manyama, Feb 20 2018

Keywords

• sign

Crossrefs

Cf. A000521, A289298.

Programs

Mathematica

CoefficientList[Series[(2 * QPochhammer[-1, x])^3 / (65536 + x*QPochhammer[-1, x]^24)^(3/8), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 20 2018 *)

Formula

Convolution inverse of A289298.

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(5/8), where c = 0.433852674132039602551793002786117867365165961976868338756... = 2^(3/8) * exp(sqrt(3) * Pi/8) * Pi^(3/2) / (3^(3/8) * Gamma(1/3)^(9/4) * Gamma(3/8)). - Vaclav Kotesovec, Feb 20 2018, updated Mar 06 2018

a(n) * A289298(n) ~ -3*2^(1/4)*sqrt(1+sqrt(2)) * exp(2*sqrt(3)*Pi*n) / (16*Pi*n^2). - Vaclav Kotesovec, Feb 20 2018