A289334 Coefficients of (q*(j(q)-1728))^(1/4) where j(q) is the elliptic modular invariant.

1, -246, -41553, -10405738, -3425019885, -1274958998550, -510099547824244, -214102720094848884, -92997705562440483771, -41448768067643091078680, -18848488732890018582016056, -8710420728901868885695224690

Offset: 0

Author

Seiichi Manyama, Jul 02 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..367

Crossrefs

(q*(j(q)-1728))^(k/24): A106203 (k=1), A289330 (k=2), A289331 (k=3), A289332 (k=4), A289333 (k=5), this sequence (k=6), A007242 (k=12), A289063 (k=24).

Cf. A289061.

Programs

Mathematica

CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(1/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)

Formula

G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/4).

a(n) ~ c * exp(2*Pi*n) / n^(3/2), where c = -3 * exp(-Pi/2) / (2^(1/2) * Gamma(3/4)^2) = -0.293663850547434552890056440879436571786655817166913678971... - Vaclav Kotesovec, Mar 07 2018