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A296614 Coefficients in expansion of (E_6^2/E_4^3)^(1/96).

%I A296614 #27 Mar 04 2018 12:40:30
%S A296614 1,-18,-1998,-1156356,-382624794,-177898412808,-76229340502932,
%T A296614 -35444571049682064,-16446161396159063082,-7832755937588033655054,
%U A296614 -3761678744155185551186328,-1828621496185972561746774324,-895757692814150533920101726460
%N A296614 Coefficients in expansion of (E_6^2/E_4^3)^(1/96).
%H A296614 Seiichi Manyama, <a href="/A296614/b296614.txt">Table of n, a(n) for n = 0..367</a>
%F A296614 G.f.: (1 - 1728/j)^(1/96).
%F A296614 a(n) ~ -Gamma(1/4)^(1/12) * exp(2*Pi*n) / (16 * 2^(1/12) * 3^(95/96) * Pi^(1/16) * Gamma(47/48) * n^(49/48)). - _Vaclav Kotesovec_, Mar 04 2018
%F A296614 a(n) * A299696(n) ~ -sin(Pi/48) * exp(4*Pi*n) / (48*Pi*n^2). - _Vaclav Kotesovec_, Mar 04 2018
%t A296614 terms = 13;
%t A296614 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A296614 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A296614 (E6[x]^2/E4[x]^3)^(1/96) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y A296614 (E_6^2/E_4^3)^(k/288): A289366 (k=1), A296609 (k=2), this sequence (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), A299413 (k=144), A289210 (k=288).
%Y A296614 Cf. A000521 (j), A299696.
%K A296614 sign
%O A296614 0,2
%A A296614 _Seiichi Manyama_, Feb 15 2018