A288727 Expansion of 1/j^2 where j is the elliptic modular invariant (A000521).

1, -1488, 1266840, -811420480, 434731407660, -205762405603104, 88869953694086720, -35768448018942261120, 13610297613250180785870, -4947238483283026511913200, 1731166476103096494953112096, -586625688530872572480200739648

Offset

2,2

Links

Seiichi Manyama, Table of n, a(n) for n = 2..420

Formula

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) * n^5, where c = 8 * Pi^24 / (5 * 3^7 * Gamma(1/3)^36) = 0.000000245024306665040229500554761856570608172017999096... - Vaclav Kotesovec, Jul 07 2017, updated Mar 05 2018

Mathematica

nmax = 20; Drop[CoefficientList[Series[((1 - (1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}])^2/(1 + 240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])^3)/1728)^2, {x, 0, nmax}], x], 2] (* Vaclav Kotesovec, Jul 07 2017 *)
a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^2, {q, 0, n}]; Table[a[n], {n, 2, 13}] (* Jean-François Alcover, Nov 02 2017 *)

Crossrefs

Cf. A000521 (j).

1/j^k: A066395 (k=1), this sequence (k=2), A289454 (k=3), A289455 (k=4).

Sequence in context: A257760 A237244 A028515 * A137705 A367769 A171617

Adjacent sequences: A288724 A288725 A288726 * A288728 A288729 A288730

Keyword

sign

Author

Seiichi Manyama, Jul 06 2017

Status

approved