A289304 Expansion of (q*j(q))^(5/12) where j(q) is the elliptic modular invariant (A000521).

1, 310, 14765, -232770, 40539830, -5199871688, 765038308115, -121140033966330, 20242157273780710, -3521886754264327670, 632344647471171938140, -116428917411726531951590, 21883035176258955622401245

Offset: 0

Author

Seiichi Manyama, Jul 02 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..425

Crossrefs

(q*j(q))^(k/24): A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), this sequence (k=10), A289305 (k=11), A161361 (k=12).

Cf. A000521, A192731.

Programs

Mathematica

CoefficientList[Series[(65536 + x*QPochhammer[-1, x]^24)^(5/4) / (2*QPochhammer[-1, x])^10, {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 23 2017 *)
(q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^(5/12) + O[q]^13 //
CoefficientList[#, q]& (* Jean-François Alcover, Nov 02 2017 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(5*A192731(n)/12).

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(9/4), where c = 0.232272469556851820006346410170543574844213494230850435863953522617... = 5 * 3^(5/4) * Gamma(1/4) * Gamma(1/3)^(15/2) / (2^(23/4) * exp(5 * Pi / (4 * sqrt(3))) * Pi^6). - Vaclav Kotesovec, Jul 03 2017, updated Mar 06 2018