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Search: id:A013974
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| A013974 |
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Eisenstein series E_10(q) (alternate convention E_5(q)). |
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+0
12
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| 1, -264, -135432, -5196576, -69341448, -515625264, -2665843488, -10653352512, -35502821640, -102284205672, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444679944
(list; graph; listen)
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OFFSET
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0,2
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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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T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Eisenstein series
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FORMULA
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sum_{n=0...infinity} a(n)/exp(Pi)^(2n) = 0 or is very close to 0. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jan 25 2005
G.f. is a period 1 Fourier series which satisfies f(-1 / t) = - (t/i)^10 * f(t) where q = exp(2 pi i t). - Michael Somos Dec 30 2008
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EXAMPLE
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1 - 264*q - 135432*q^2 - 5196576*q^3 - 69341448*q^4 - 515625264*q^5 + ...
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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(10);
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PROGRAM
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(PARI) a(n)=if(n<1, n==0, -264*sigma(n, 9))
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CROSSREFS
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Cf. A008410.
Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (E_12), A058550 (E_14), A029829 (E_16), A029830 (E_20), A029831 (E_24).
Convolution of A004009 and A013973.
Sequence in context: A022043 A035315 A107507 this_sequence A145639 A116501 A151602
Adjacent sequences: A013971 A013972 A013973 this_sequence A013975 A013976 A013977
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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