A289454 Expansion of 1/j^3 where j is the elliptic modular invariant (A000521).

1, -2232, 2730564, -2425008768, 1748443340826, -1085940040502592, 602376210735356376, -305671359557586479616, 144309502321265349235035, -64175062238369552680712096, 27135987216939727366492175940, -10990160397215122310079248998656

Offset

3,2

Links

Seiichi Manyama, Table of n, a(n) for n = 3..419

Formula

a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) * n^8, where c = (4*Pi^36) / (35 * 3^11 * Gamma(1/3)^54) = 0.00000000000395425888452699792549199102489774693818147819519... - 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)^3, {x, 0, nmax}], x], 3] (* Vaclav Kotesovec, Jul 07 2017 *)
a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^3, {q, 0, n}]; Table[a[n], {n, 3, 14}] (* Jean-François Alcover, Nov 02 2017 *)

Crossrefs

Cf. A000521 (j).

1/j^k: A066395 (k=1), A288727 (k=2), this sequence (k=3), A289455 (k=4), A289512 (k=5), A289513(k=6), A289514 (k=7), A289515 (k=8), A289516 (k=9), A289517 (k=10).

Sequence in context: A205038 A279661 A288846 * A378563 A372248 A079013

Adjacent sequences: A289451 A289452 A289453 * A289455 A289456 A289457

Keyword

sign

Author

Seiichi Manyama, Jul 06 2017

Status

approved