|
Search: id:A027653
|
|
|
| A027653 |
|
Values of Zagier's function J_1(k) as k runs through the numbers -1, 0, 3, 4, 7, 8, ... which are == -1 or 0 mod 4. |
|
+0
5
|
|
| -1, 2, -248, 492, -4119, 7256, -33512, 53008, -192513, 287244, -885480, 1262512, -3493982, 4833456, -12288992, 16576512, -39493539, 52255768, -117966288, 153541020, -331534572, 425691312, -884736744, 1122626864, -2257837845, 2835861520, -5541103056, 6896878512
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
That is, a(n) = J_1(k) where k is the n-th number >= -1 which is == -1 or 0 mod 4.
|
|
REFERENCES
|
M. Kaneko, The Fourier coefficients and the singular moduli of the elliptic modular function j(tau), Memoirs Faculty Engin. Sci., Kyoto Inst. Technology, 44 (March 1996), pp. 1-5.
M. Kaneko, Fourier coefficients of the elliptic modular function j(tau) (in Japanese), Rokko Lectures in Mathematics 10, Dept. Math., Faculty of Science, Kobe University, Rokko, Kobe, Japan, 2001.
|
|
LINKS
|
N. J. A. Sloane, Table of n, a(n) for n = 1..1002
|
|
FORMULA
|
For recurrence see Maple code.
|
|
MAPLE
|
with(numtheory); M:=30; t[ -1]:=-1; t[0]:=2;
for n from 1 to M do
t[4*n-1]:=-240*sigma[3](n)-add( r^2*t[4*n-r^2], r=2..floor(sqrt(4*n+1)));
t[4*n]:=-2*add( t[4*n-r^2], r=1..floor(sqrt(4*n+1)));
lprint(t[4*n-1], t[4*n]); od:
|
|
CROSSREFS
|
Cf. A027652, A027654, A027655, A014708, A007240, A000521.
Sequence in context: A065664 A024031 A099685 this_sequence A024349 A012529 A012527
Adjacent sequences: A027650 A027651 A027652 this_sequence A027654 A027655 A027656
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
Entry revised by njas, Jul 24 2006
|
|
|
Search completed in 0.002 seconds
|
