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A058552
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Numerators of q-expansion of Eisenstein series E_16(q).
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1
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1, 16320, 534790080, 234174178560, 17524001357760, 498046875016320, 7673653657232640, 77480203842286080, 574226476491096000, 3360143509958850240, 16320498047409790080, 68172690124863440640, 251450283274373326080
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OFFSET
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0,2
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COMMENTS
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Denominators are 3617 except for leading term for which denominator is 1.
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REFERENCES
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R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 53.
N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 1984, see p. 111.
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LINKS
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MAPLE
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E := proc(k) local n, t1; t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..60); series(t1, q, 60); end; E(16);
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MATHEMATICA
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terms = 13; E16[x_] = 1 - (32/BernoulliB[16])*Sum[k^15*(x^k/(1 - x^k)), {k, 1, terms}]; E16[x] + O[x]^terms // CoefficientList[#, x]& // Numerator (* Jean-François Alcover, Feb 27 2018 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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