|
| |
|
|
A035314
|
|
Fourier coefficients of T_8.
|
|
0
|
|
|
|
1, -480, -28404, -682240, -10460070, -120178944, -1122367480, -8942109696, -62733463065, -396222777600, -2289950627940, -12261279536640, -61415457336714, -290017200522240, -1299352388589720, -5552275006294016, -22728781503345645, -89469772048615680
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
-1,2
|
|
|
COMMENTS
|
T_8 is the unique weight = -6 normalized meromorphic modular form for SL(2,Z) with all poles at infinity.
|
|
|
REFERENCES
|
C.L. Siegel, Advanced Analytic Number Theory,Tata Institute of Fundamental Research, Bombay, 1980, pp. 249-268.
|
|
|
LINKS
|
Table of n, a(n) for n=-1..16.
|
|
|
FORMULA
|
Gen. fcn. = G_6/Delta (in Siegel's notation.)
|
|
|
EXAMPLE
|
T_8 = 1/q - 480 - 28404 q - ....
|
|
|
PROG
|
(PARI) {a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff( sum(k=1, n, -504*sigma(k, 5)*x^k, 1+A)/eta(x+A)^24, n))} /* Michael Somos Oct 30 2006 */
|
|
|
CROSSREFS
|
Sequence in context: A199808 A199809 A063870 * A022047 A107511 A008410
Adjacent sequences: A035311 A035312 A035313 * A035315 A035316 A035317
|
|
|
KEYWORD
|
easy,sign
|
|
|
AUTHOR
|
Barry Brent (barryb(AT)primenet.com)
|
|
|
STATUS
|
approved
|
| |
|
|
