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A076835
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Coefficients in expansion of Eisenstein series -q*E'_2.
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9
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24, 144, 288, 672, 720, 1728, 1344, 2880, 2808, 4320, 3168, 8064, 4368, 8064, 8640, 11904, 7344, 16848, 9120, 20160, 16128, 19008, 13248, 34560, 18600, 26208, 25920, 37632, 20880, 51840, 23808, 48384, 38016, 44064, 40320, 78624, 33744, 54720, 52416, 86400
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OFFSET
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1,1
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LINKS
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FORMULA
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q*E'_2 = (E_2^2-E_4)/12.
G.f.: 24*x*f'(x), where f(x) = Sum_{k>=1} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Aug 31 2017
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EXAMPLE
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G.f. = 24*q + 144*q^2 + 288*q^3 + 672*q^4 + 720*q^5 + ...
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MAPLE
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with(numtheory); E:=proc(k) series(1-(2*k/bernoulli(k))*add( sigma[k-1](n)*q^n, n=1..60), q, 61); end; -diff(E(2), q);
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MATHEMATICA
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terms = 41;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
-(E2[x]^2 - E4[x])/12 + O[x]^terms // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Feb 23 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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