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A299862 Coefficients in expansion of (E_6^2/E_4^3)^(1/32).

%I A299862 #16 Mar 04 2018 08:12:28
%S A299862 1,-54,-5022,-3259116,-1012953978,-479848911192,-201506019745716,
%T A299862 -93655132040105136,-43096009052844972522,-20449878102745826555178,
%U A299862 -9772372681245342509703768,-4732826670479844302345499132,-2309711500786845517082643561660
%N A299862 Coefficients in expansion of (E_6^2/E_4^3)^(1/32).
%H A299862 Seiichi Manyama, <a href="/A299862/b299862.txt">Table of n, a(n) for n = 0..367</a>
%F A299862 G.f.: (1 - 1728/j)^(1/32), where j is the j-function.
%F A299862 a(n) ~ c * exp(2*Pi*n) / n^(17/16), where c = -3^(1/32) * Gamma(1/4)^(1/4) / (2^(17/4) * Pi^(3/16) * Gamma(15/16)) = -0.0582176906417343821471376177620947... - _Vaclav Kotesovec_, Mar 04 2018
%F A299862 a(n) * A299949(n) ~ -sin(Pi/16) * exp(4*Pi*n) / (16*Pi*n^2). - _Vaclav Kotesovec_, Mar 04 2018
%t A299862 terms = 13;
%t A299862 E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
%t A299862 E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t A299862 (E6[x]^2/E4[x]^3)^(1/32) + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 28 2018 *)
%Y A299862 (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), this sequence (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 A299862 Cf. A000521 (j).
%K A299862 sign
%O A299862 0,2
%A A299862 _Seiichi Manyama_, Feb 21 2018