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A145095
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Coefficients in expansion of Eisenstein series -q*E'_6.
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9
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504, 33264, 368928, 2130912, 7877520, 24349248, 59298624, 136382400, 268953048, 519916320, 892872288, 1559827584, 2432718288, 3913709184, 5766344640, 8728481664, 12165343344, 17750901168, 23711133600, 33306154560, 43406592768, 58929571008
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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'_6 = (E_2*E_6-E_4^2)/2.
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EXAMPLE
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G.f. = 504*q + 33264*q^2 + 368928*q^3 + 2130912*q^4 + 7877520*q^5 + ...
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MATHEMATICA
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terms = 23;
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}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
-(E2[x]*E6[x] - E4[x]^2)/2 + 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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