%I #40 Mar 04 2018 17:36:59
%S 1,-864,269568,-75240576,19930724352,-5124295980864,1292387210099712,
%T -321604751662509312,79241739168490536960,-19376923061550541800672,
%U 4709786462808256974509568,-1139188440993923671697455488
%N Coefficients in expansion of (E_6^2/E_4^3)^(1/2).
%H Seiichi Manyama, <a href="/A299413/b299413.txt">Table of n, a(n) for n = 0..422</a>
%F G.f.: (1 - 1728/j)^(1/2), where j is the j-function.
%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) * sqrt(n), where c = 32*sqrt(2) * Pi^(11/2) / Gamma(1/3)^9. - _Vaclav Kotesovec_, Mar 04 2018
%t terms = 12;
%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}] + O[x]^terms;
%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}] + O[x]^terms; (E6[x]^2/E4[x]^3)^(1/2) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 22 2018 *)
%Y (E_6^2/E_4^3)^(k/288): A289366 (k=1), A296609 (k=2), A296614 (k=3), A296652 (k=4), A297021 (k=6), A299422 (k=8), A299862 (k=9), A289368 (k=12), A299856 (k=16), A299857 (k=18), A299858 (k=24), A299863 (k=32), A299859 (k=36), A299860 (k=48), A299861 (k=72), A299414 (k=96), this sequence (k=144), A289210 (k=288).
%Y Cf. A000521 (j), A007242, A299832.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 21 2018