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%I #23 Mar 06 2018 10:57:32
%S 1,-31,3809,-620190,111669570,-21246138749,4186228503780,
%T -845058129488699,173647689528542310,-36170751826552656600,
%U 7615730581866678419370,-1617501058117655447210580,346019784662582818549094159
%N Coefficients in expansion of (q*j(q))^(-1/24).
%H Seiichi Manyama, <a href="/A289397/b289397.txt">Table of n, a(n) for n = 0..424</a>
%F G.f.: Product_{n>=1} (1-q^n)^(-A192731(n)/24) = Product_{n>=1} (1-q^n)^(1-A289395(n)).
%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(7/8), where c = 0.13397834215417716857261649901051678539339753563926756586381... = 2^(1/8) * exp(Pi/(8 * sqrt(3))) * sqrt(Pi) / (3^(1/8) * Gamma(1/8) * Gamma(1/3)^(3/4)). - _Vaclav Kotesovec_, Mar 05 2018, updated Mar 06 2018
%F a(n) * A106205(n) ~ c * exp(2*Pi*sqrt(3)*n) / n^2, where c = -sqrt(2-sqrt(2)) / (16*Pi). - _Vaclav Kotesovec_, Mar 06 2018
%t (q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^(-1/24) + O[q]^13 // CoefficientList[#, q]& (* _Jean-François Alcover_, Nov 02 2017 *)
%Y (q*j(q))^(k/24): this sequence (k=-1), A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), A289304 (k=10), A289305 (k=11), A161361 (k=12).
%Y Cf. A000521 (j(q)), A066395.
%K sign
%O 0,2
%A _Seiichi Manyama_, Jul 05 2017
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