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A145094
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Coefficients in expansion of Eisenstein series q*E'_4.
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11
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240, 4320, 20160, 70080, 151200, 362880, 577920, 1123200, 1635120, 2721600, 3516480, 5886720, 6857760, 10402560, 12700800, 17975040, 20049120, 29432160, 31281600, 44150400, 48545280, 63296640, 67167360, 94348800, 94506000, 123439680, 132451200
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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'_4 = (E_2*E_4-E_6)/3.
G.f.: 240*x*f'(x), where f(x) = Sum_{k>=1} k^3*x^k/(1 - x^k). - Ilya Gutkovskiy, Aug 31 2017
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EXAMPLE
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G.f. = 240*q + 4320*q^2 + 20160*q^3 + 70080*q^4 + 151200*q^5 + ...
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MATHEMATICA
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terms = 28;
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]*E4[x] - E6[x])/3 + 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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