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 A066395 Expansion of reciprocal of j-function (see A000521). 17

%I

%S 1,-744,356652,-140361152,49336682190,-16114625669088,

%T 4999042477430456,-1492669384085015040,432762759484818142437,

%U -122566701136436206749360,34058364214245581228710692,-9315629487329800685570383104,2514284824201628853303708453062

%N Expansion of reciprocal of j-function (see A000521).

%H Seiichi Manyama, <a href="/A066395/b066395.txt">Table of n, a(n) for n = 1..421</a>

%H Y. Abdelaziz, J.-M. Maillard, <a href="https://arxiv.org/abs/1611.08493">Modular forms, Schwarzian conditions, and symmetries of differential equations in physics</a>, arXiv preprint arXiv:1611.08493 [math-ph], 2016.

%F 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

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

%t 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 *)

%t 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 *)

%K sign

%O 1,2

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

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Last modified October 18 22:03 EDT 2019. Contains 328211 sequences. (Running on oeis4.)