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%I #26 Feb 26 2018 10:18:53
%S 1,-1008,220752,16519104,399517776,4624512480,34423752384,
%T 187506813312,814794618960,2975666040144,9486668147040,27052407031104,
%U 70486610910912,169931677686624,384163181281152,820165393918080,1668889095288912,3249638073414432
%N Expansion of E_6(q)^2 in powers of q.
%H Seiichi Manyama, <a href="/A280869/b280869.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EisensteinSeries.html">Eisenstein Series.</a>
%F E6(q)^2 = (1 - 504 Sum_{i>=1} sigma_5(i)q^i)^2 where sigma_5(n) is A001160.
%F A008411(n) - a(n) = 1728*A000594(n).
%F A029828(n) - 691*a(n) = 762048*A000594(n).
%F A029828(n) = 441*A008411(n) + 250*a(n).
%e G.f. = 1 - 1008*q + 220752*q^2 + 16519104*q^3 + 399517776*q^4 + 4624512480*q^5 + ...
%t terms = 18;
%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
%t E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 26 2018 *)
%Y Cf. A000594, A001160, A008411, A013973 (E_6), A029828 (691*E_12).
%K sign
%O 0,2
%A _Seiichi Manyama_, Jan 28 2017
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