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A037944
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Coefficients of unique normalized cusp form Delta_18 of weight 18 for full modular group.
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4
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1, -528, -4284, 147712, -1025850, 2261952, 3225992, -8785920, -110787507, 541648800, -753618228, -632798208, 2541064526, -1703323776, 4394741400, -14721941504, -5429742318, 58495803696, 1487499860, -151530355200
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: 691/(1728*250) * (E_4(q)*E_14(q) - E_6(q)*E_12(q)). - Seiichi Manyama, Jul 25 2017
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EXAMPLE
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G.f. = q - 528*q^2 - 4284*q^3 + 147712*q^4 - 1025850*q^5 + 2261952*q^6 + ...
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MATHEMATICA
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terms = 20;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms+1}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms+1}];
E12[x_] = 1 + (65520/691)*Sum[k^11*x^k/(1 - x^k), {k, 1, terms}];
E14[x_] = 1 - 24*Sum[k^13*x^k/(1 - x^k), {k, 1, terms}];
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PROG
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(PARI) {a(n) = if( n<0, 0, polcoeff( x * eta(x + x * O(x^n))^24 * (1 - 504 * sum( k=1, n, sigma( k, 5) * x^k)), n))}; /* Michael Somos, Mar 18 2012 */
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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