|
Search: id:A006352
|
|
|
| A006352 |
|
Coefficients in expansion of Eisenstein series E_2 (also called E_1 or G_2).
(Formerly M5145)
|
|
+0
16
|
|
| 1, -24, -72, -96, -168, -144, -288, -192, -360, -312, -432, -288, -672, -336, -576, -576, -744, -432, -936, -480, -1008, -768, -864, -576, -1440, -744, -1008, -960, -1344, -720, -1728, -768, -1512, -1152, -1296, -1152, -2184, -912, -1440, -1344, -2160, -1008, -2304, -1056, -2016, -1872, -1728
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Expansion of Ramanujan's function P(q).
|
|
REFERENCES
|
F. Beukers, Another congruence for the Apery numbers. J. Number Theory 25 (1987), no. 2, 201-210.
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 pp. 111 and 113.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..1000
H. Ochiai, Counting functions for branched covers of elliptic curves and quasi-modular forms
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Eisenstein series
|
|
FORMULA
|
n-th term is -24*sigma(n), for n>0.
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=u1^2+4*u2^2+9*u3^2+36*u6^2-8*u1*u2+6*u1*u3+24*u2*u6-72*u3*u6 . - Michael Somos May 29 2005
G.f.: 1-24(Sum_{k>0} kx^k/(1-x^k)).
|
|
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(2);
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, n==0, -24*sigma(n))
|
|
CROSSREFS
|
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).
Sequence in context: A069174 A124717 A126378 this_sequence A090860 A064200 A042128
Adjacent sequences: A006349 A006350 A006351 this_sequence A006353 A006354 A006355
|
|
KEYWORD
|
sign,easy,nice
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
|
|
|
Search completed in 0.002 seconds
|
