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
Seiichi Manyama, Table of n, a(n) for n = -1..1000
FORMULA
G.f.: G_6/Delta (in Siegel's notation).
a(n) ~ -exp(4*Pi*sqrt(n)) / (sqrt(2) * n^(15/4)). - Vaclav Kotesovec, Oct 04 2020
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
KEYWORD
easy,sign
AUTHOR
Barry Brent (barryb(AT)primenet.com)
STATUS
approved