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%I #20 Mar 04 2018 12:45:00
%S 1,-432,41472,-19704384,593104896,-1488746462112,-215673487239168,
%T -180545262418802304,-58940991594820435968,-31030127172303490499184,
%U -13143520096697989968012288,-6336110261914309914844683456
%N Coefficients in expansion of (E_6^2/E_4^3)^(1/4).
%H Seiichi Manyama, <a href="/A299861/b299861.txt">Table of n, a(n) for n = 0..367</a>
%F G.f.: (1 - 1728/j)^(1/4), where j is the j-function.
%F a(n) ~ -3^(1/4) * Gamma(1/4)^2 * exp(2*Pi*n) / (8 * Pi^2 * n^(3/2)). - _Vaclav Kotesovec_, Mar 04 2018
%F a(n) * A300053(n) ~ -exp(4*Pi*n) / (2*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}];
%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t (E6[x]^2/E4[x]^3)^(1/4) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 28 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), this sequence (k=72), A299414 (k=96), A299413 (k=144), A289210 (k=288).
%Y Cf. A000521 (j), A289334, A299830.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 21 2018
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