A066396 Reversion of j-function (see A000521).

1, -744, 910188, -1348239200, 2212373200878, -3870035739603792, 7072625493441991016, -13343943944697578921664, 25793763474486715046892405, -50818736423094538469855431992, 101675138631197524697523625818636, -206021386741542411973931322075432864

Offset

-1,2

Comments

To get Maple to produce this, form t := series expansion of q^2 * j, and then do solve(t=y, y).

Links

Andrew Howroyd, Table of n, a(n) for n = -1..100

N. J. A. Sloane, Transforms

Index entries for reversions of series

Formula

a(n) ~ c * (-1)^(n+1) * d^n / n^(3/2), where d = 2311.394562122568826864554431309352700589081544164805515755738565159053682... and c = 1943.54943209790549766737504313567156926515672546456731498696867555099... - Vaclav Kotesovec, Jun 28 2017, updated Mar 07 2018

Example

If we write t = q^2*j = x + 744*x^2 + 196884*x^3 + ..., then x = t - 744*t^2 + 910188*t^3 - ...

Mathematica

f[q_] = q^2*1728*KleinInvariantJ[ Log[q]/(2*Pi*I) ]; Rest[ CoefficientList[ InverseSeries[ Series[ f[q], {q, 0, 12}] ], q] ] (* Jean-François Alcover, Feb 17 2012 *)

Prog

(PARI) Vec(serreverse(q^2*ellj(q+O(q^15)))) \\ Joerg Arndt, Feb 25 2012

Crossrefs

Cf. A000521. See A091406 for another version.

Sequence in context: A161557 A294182 A091406 * A099819 A344014 A051978

Adjacent sequences: A066393 A066394 A066395 * A066397 A066398 A066399

Keyword

sign

Author

N. J. A. Sloane, Dec 24 2001

Extensions

b-file corrected by Andrew Howroyd, Feb 23 2018

Status

approved