A289333 Coefficients of (q*(j(q)-1728))^(5/24) where j(q) is the elliptic modular invariant.

1, -205, -38830, -10493215, -3586921610, -1369515719416, -558606292282075, -238153389340570570, -104811899537297598195, -47246821512435762941195, -21700419062680514765163503, -10118052721530705778119535745

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

G.f.: Product_{k>=1} (1-q^k)^(5*A289061(k)/24).

a(n) ~ c * exp(2*Pi*n) / n^(17/12), where c = -5 * 3^(1/3) * Gamma(2/3)^2 * exp(-5*Pi/12) * Gamma(1/12) / (2^(49/12) * Pi^(19/12) * Gamma(3/4)^(5/3)) = -0.28184482434015938133067183460309604452260645657140372869996481157015... - Vaclav Kotesovec, Mar 07 2018

Mathematica

CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(5/24), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)

Crossrefs

(q*(j(q)-1728))^(k/24): A106203 (k=1), A289330 (k=2), A289331 (k=3), A289332 (k=4), this sequence (k=5), A289334 (k=6), A007242 (k=12), A289063 (k=24).

Cf. A289061.

Sequence in context: A060892 A359498 A203862 * A015289 A203888 A188447

Adjacent sequences: A289330 A289331 A289332 * A289334 A289335 A289336

Keyword

sign

Author

Seiichi Manyama, Jul 02 2017

Status

approved