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 A280869 Expansion of E_6(q)^2 in powers of q. 17
 1, -1008, 220752, 16519104, 399517776, 4624512480, 34423752384, 187506813312, 814794618960, 2975666040144, 9486668147040, 27052407031104, 70486610910912, 169931677686624, 384163181281152, 820165393918080, 1668889095288912, 3249638073414432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Eisenstein Series. FORMULA E6(q)^2 = (1 - 504 Sum_{i>=1} sigma_5(i)q^i)^2 where sigma_5(n) is A001160. A008411(n) - a(n) = 1728*A000594(n). A029828(n) - 691*a(n) = 762048*A000594(n). A029828(n) = 441*A008411(n) + 250*a(n). EXAMPLE G.f. = 1 - 1008*q + 220752*q^2 + 16519104*q^3 + 399517776*q^4 + 4624512480*q^5 + ... MATHEMATICA terms = 18; E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}]; E6[x]^2 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *) CROSSREFS Cf. A000594, A001160, A008411, A013973 (E_6), A029828 (691*E_12). Sequence in context: A331770 A290286 A187863 * A145235 A210759 A171119 Adjacent sequences:  A280866 A280867 A280868 * A280870 A280871 A280872 KEYWORD sign AUTHOR Seiichi Manyama, Jan 28 2017 STATUS approved

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Last modified May 16 20:11 EDT 2022. Contains 353720 sequences. (Running on oeis4.)