A066395 Expansion of reciprocal of j-function (see A000521).

1, -744, 356652, -140361152, 49336682190, -16114625669088, 4999042477430456, -1492669384085015040, 432762759484818142437, -122566701136436206749360, 34058364214245581228710692, -9315629487329800685570383104, 2514284824201628853303708453062

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..421

Y. Abdelaziz, J.-M. Maillard, Modular forms, Schwarzian conditions, and symmetries of differential equations in physics, arXiv preprint arXiv:1611.08493 [math-ph], 2016.

Formula

a(n) ~ c * (-1)^(n+1) * exp(Pi*sqrt(3)*n) * n^2, where c = 4*Pi^12 / (27*Gamma(1/3)^18) = 0.00271122282373677410826992857036010754653235515106627... - Vaclav Kotesovec, Jun 28 2017, updated Mar 03 2018

Example

q*(1 - 744*q + 356652*q^2 - 140361152*q^3 + 49336682190*q^4 - 16114625669088*q^5 + ...).

Mathematica

nmax = 20; Rest[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, {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jul 07 2017 *)
a[n_] := SeriesCoefficient[1/(1728*KleinInvariantJ[-Log[q]*I/(2*Pi)]), {q, 0, n}]; Table[a[n], {n, 1, 13}] (* Jean-François Alcover, Nov 02 2017 *)

Crossrefs

Sequence in context: A000521 A178449 A178451 * A161557 A294182 A091406

Adjacent sequences: A066392 A066393 A066394 * A066396 A066397 A066398

Keyword

sign

Author

N. J. A. Sloane, Dec 24 2001

Status

approved