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A058552 Numerators of q-expansion of Eisenstein series E_16(q). 1
1, 16320, 534790080, 234174178560, 17524001357760, 498046875016320, 7673653657232640, 77480203842286080, 574226476491096000, 3360143509958850240, 16320498047409790080, 68172690124863440640, 251450283274373326080 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Denominators are 3617 except for leading term for which denominator is 1.
REFERENCES
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.
LINKS
MAPLE
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);
MATHEMATICA
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 *)
CROSSREFS
Cf. A029829.
Sequence in context: A043607 A067375 A237460 * A337417 A013690 A247826
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Dec 25 2000
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)