A289397 Coefficients in expansion of (q*j(q))^(-1/24).

1, -31, 3809, -620190, 111669570, -21246138749, 4186228503780, -845058129488699, 173647689528542310, -36170751826552656600, 7615730581866678419370, -1617501058117655447210580, 346019784662582818549094159

Offset: 0

Author

Seiichi Manyama, Jul 05 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..424

Crossrefs

(q*j(q))^(k/24): this sequence (k=-1), 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), A289304 (k=10), A289305 (k=11), A161361 (k=12).

Cf. A000521 (j(q)), A066395.

Programs

Mathematica

(q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^(-1/24) + O[q]^13 // CoefficientList[#, q]& (* Jean-François Alcover, Nov 02 2017 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(-A192731(n)/24) = Product_{n>=1} (1-q^n)^(1-A289395(n)).

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(7/8), where c = 0.13397834215417716857261649901051678539339753563926756586381... = 2^(1/8) * exp(Pi/(8 * sqrt(3))) * sqrt(Pi) / (3^(1/8) * Gamma(1/8) * Gamma(1/3)^(3/4)). - Vaclav Kotesovec, Mar 05 2018, updated Mar 06 2018

a(n) * A106205(n) ~ c * exp(2*Pi*sqrt(3)*n) / n^2, where c = -sqrt(2-sqrt(2)) / (16*Pi). - Vaclav Kotesovec, Mar 06 2018