%I #32 Mar 04 2018 12:45:28
%S 1,-576,96768,-30253824,4526272512,-1917275819904,105679295281152,
%T -161582272076127744,-20815321809392861184,-20529723592970845750080,
%U -6560883968194298456036352,-3617226648349298247150473472
%N Coefficients in expansion of (E_6^2/E_4^3)^(1/3).
%H Seiichi Manyama, <a href="/A299414/b299414.txt">Table of n, a(n) for n = 0..367</a>
%F G.f.: (1 - 1728/j)^(1/3), where j is the j-function.
%F a(n) ~ -Gamma(1/4)^(8/3) * exp(2*Pi*n) / (2^(5/3) * 3^(2/3) * Pi^2 * Gamma(1/3) * n^(5/3)). - _Vaclav Kotesovec_, Mar 04 2018
%F a(n) * A300054(n) ~ -exp(4*Pi*n) / (sqrt(3)*Pi*n^2). - _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)^(1/3) + 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), this sequence (k=96), A299413 (k=144), A289210 (k=288).
%Y Cf. A000521 (j), A289340, A299831.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 21 2018