A035315 Fourier coefficients of T_{10}.

1, 264, 8244, 139520, 1672290, 15872256, 126745880, 884100096, 5525046495, 31498809600, 166049246340, 817866616320, 3794952949854, 16699329285120, 70071039813240, 281650911606784, 1088671630120515, 4060062852952320

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

Seiichi Manyama, Table of n, a(n) for n = -1..1000

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

Adjacent sequences: A035312 A035313 A035314 * A035316 A035317 A035318

Keyword

easy,nonn

Author

Barry Brent (barryb(AT)primenet.com)

Status

approved