A289455 Expansion of 1/j^4 where j is the elliptic modular invariant (A000521).

1, -2976, 4747824, -5392956800, 4889133749400, -3761165322168768, 2549962294786430144, -1562849905009064897280, 881746577453401952409900, -464149085470990004575901600, 230323243751761513144853469408, -108618796884881830752241855604352

Offset

4,2

Links

Seiichi Manyama, Table of n, a(n) for n = 4..418

Formula

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) * n^11, where c = 16 * Pi^48 / (82864937925 * Gamma(1/3)^72) = 0.00000000000000002165833724988588666420880993216216369751685... - 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)^4, {x, 0, nmax}], x], 4] (* Vaclav Kotesovec, Jul 07 2017 *)
a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^4, {q, 0, n}]; Table[a[n], {n, 4, 15}] (* Jean-François Alcover, Nov 02 2017 *)

Crossrefs

Cf. A000521 (j).

1/j^k: A066395 (k=1), A288727 (k=2), A289454 (k=3), this sequence (k=4).

Sequence in context: A186549 A236140 A281330 * A360666 A202775 A235744

Adjacent sequences: A289452 A289453 A289454 * A289456 A289457 A289458

Keyword

sign

Author

Seiichi Manyama, Jul 06 2017

Status

approved