A289331 Coefficients of (q*(j(q)-1728))^(1/8) where j(q) is the elliptic modular invariant.

1, -123, -28341, -8688812, -3182839959, -1275218435124, -539854235696065, -237249494737728429, -107125917871853210346, -49374268015554366062883, -23126111889684391337303994, -10973394463170114841113101133

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), this sequence (k=3), A289332 (k=4), A289333 (k=5), A289334 (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)^(1/8), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)

Formula

G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/8).

a(n) ~ c * exp(2*Pi*n) / n^(5/4), where c = -3^(1/2) * Pi^(1/4) * exp(-Pi/4) / (2^(7/4) * Gamma(3/4)^2) = -0.20815359871514720517220474749202446933362532... - Vaclav Kotesovec, Mar 07 2018