login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A035315 Fourier coefficients of T_{10}. 3
1, 264, 8244, 139520, 1672290, 15872256, 126745880, 884100096, 5525046495, 31498809600, 166049246340, 817866616320, 3794952949854, 16699329285120, 70071039813240, 281650911606784, 1088671630120515, 4060062852952320 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,2
COMMENTS
T_{10} is the unique weight = -8 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
Borcherds, Richard E., Automorphic forms with singularities on Grassmannians, Invent. Math. 132 (1998), 491-562.
FORMULA
G.f.: G_4/Delta (in Siegel's notation.)
a(n) ~ exp(4*Pi*sqrt(n)) / (sqrt(2) * n^(19/4)). - Vaclav Kotesovec, Oct 04 2020
EXAMPLE
T_{10} = 1/q + 264 + 8244 q + ....
PROG
(PARI) {a(n)=if(n<-1, 0, n++; polcoeff( sum(k=1, n, 240*sigma(k, 3)*x^k, 1+x*O(x^n))/eta(x+x*O(x^n))^24, n))} /* Michael Somos, Apr 12 2005 */
CROSSREFS
Sequence in context: A282781 A223339 A022043 * A288877 A278409 A168196
KEYWORD
easy,nonn
AUTHOR
Barry Brent (barryb(AT)primenet.com)
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 07:20 EDT 2024. Contains 371235 sequences. (Running on oeis4.)