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A066396 Reversion of j-function (see A000521). 5

%I

%S 1,-744,910188,-1348239200,2212373200878,-3870035739603792,

%T 7072625493441991016,-13343943944697578921664,

%U 25793763474486715046892405,-50818736423094538469855431992,101675138631197524697523625818636,-206021386741542411973931322075432864

%N Reversion of j-function (see A000521).

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

%H Andrew Howroyd, <a href="/A066396/b066396.txt">Table of n, a(n) for n = -1..100</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F 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

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

%t f[q_] = q^2*1728*KleinInvariantJ[ Log[q]/(2*Pi*I) ]; Rest[ CoefficientList[ InverseSeries[ Series[ f[q], {q, 0, 12}] ], q] ] (* _Jean-Fran├žois Alcover_, Feb 17 2012 *)

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

%Y Cf. A000521. See A091406 for another version.

%K sign

%O -1,2

%A _N. J. A. Sloane_, Dec 24 2001

%E b-file corrected by _Andrew Howroyd_, Feb 23 2018

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Last modified September 16 10:36 EDT 2019. Contains 327094 sequences. (Running on oeis4.)