A289339 Coefficients of (q*(j(q)-1728))^(7/24) where j(q) is the elliptic modular invariant.

1, -287, -42595, -9750370, -3081185660, -1117168154431, -438204467218406, -181018051263504195, -77584080248087108885, -34183723168674046275385, -15388633770558568711781905, -7047808475666778827478858184

Offset

0,2

Links

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

Formula

G.f.: Product_{k>=1} (1-q^k)^(7*A289061(k)/24).

a(n) ~ c * exp(2*Pi*n) / n^(19/12), where c = -7 * exp(-7*Pi/12) * Gamma(1/12) / (2^(35/12) * 3^(1/12) * Pi^(17/12) * Gamma(3/4)^(1/3)) = -0.287342744567300675294730727139553541489784437990631575713791583301655... - Vaclav Kotesovec, Mar 07 2018

Mathematica

CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(7/24), {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), A289333 (k=5), A289334 (k=6), this sequence (k=7), A289340 (k=8), A007242 (k=12), A289063 (k=24).

Cf. A289061.

Sequence in context: A236869 A158287 A112245 * A011817 A334008 A035882

Adjacent sequences: A289336 A289337 A289338 * A289340 A289341 A289342

Keyword

sign

Author

Seiichi Manyama, Jul 02 2017

Status

approved