A299826 Coefficients in expansion of (q*j(q))^(-1/12) where j(q) is the elliptic modular invariant (A000521).

1, -62, 8579, -1476538, 276299401, -54140398258, 10925052030358, -2250028212438240, 470403050272649518, -99482921702360817662, 21231436164082720565341, -4564732260005808181200000, 987422026920066412423809840

Offset: 0

Author

Seiichi Manyama, Feb 20 2018

Keywords

• sign

Crossrefs

(q*j(q))^(k/24): A289397 (k=-1), this sequence (k=-2), A299827 (k=-3), A299828 (k=-4), A299829 (k=-5), A299830 (k=-6), A299831 (k=-8), A299832 (k=-12).

Cf. A000521, A289297.

Programs

Mathematica

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

Formula

Convolution inverse of A289297.

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(3/4), where c = 0.28101701912289268934379724324854717406285519051128823261445... = 2^(1/4) * exp(Pi/(4 * sqrt(3))) * Pi / (3^(1/4) * Gamma(1/4) * Gamma(1/3)^(3/2)). - Vaclav Kotesovec, Feb 20 2018, updated Mar 06 2018

a(n) * A289297(n) ~ -exp(2*sqrt(3)*n*Pi) / (2^(5/2)*Pi*n^2). - Vaclav Kotesovec, Feb 20 2018