|
| |
|
|
A013974
|
|
Eisenstein series E_10(q) (alternate convention E_5(q)).
|
|
12
| |
|
|
1, -264, -135432, -5196576, -69341448, -515625264, -2665843488, -10653352512, -35502821640, -102284205672, -264515760432, -622498190688, -1364917062432, -2799587834736, -5465169838656, -10149567696576, -18177444679944
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
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
| 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
|
|
|
FORMULA
| 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
|
|
|
EXAMPLE
| 1 - 264*q - 135432*q^2 - 5196576*q^3 - 69341448*q^4 - 515625264*q^5 + ...
|
|
|
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(10);
|
|
|
PROG
| (PARI) a(n)=if(n<1, n==0, -264*sigma(n, 9))
|
|
|
CROSSREFS
| 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: A035315 A168196 A107507 * A145639 A116501 A151602
Adjacent sequences: A013971 A013972 A013973 * A013975 A013976 A013977
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
