A035293 Fourier coefficients of T_6.

1, 504, 73764, 2695040, 54755730, 778640256, 8638286840, 79534711296, 632179869615, 4456706505600, 28415446027380, 166276832866560, 903193785328974, 4595374951395840, 22061107725128280, 100534965940777984

Offset

-1,2

Comments

T_6 is the unique weight = -4 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_8/Delta (in Siegel's notation).

G.f.: E_4^2 / Delta where Delta = eta(q)^24. - Sean A. Irvine, Oct 03 2020

a(n) ~ exp(4*Pi*sqrt(n)) / (sqrt(2) * n^(11/4)). - Vaclav Kotesovec, Oct 04 2020

Example

T_6 = 1/q + 504 + 73764 q + ....

Crossrefs

Cf. A004009, A035281.

Sequence in context: A012744 A291116 A145095 * A278626 A288851 A105097

Adjacent sequences: A035290 A035291 A035292 * A035294 A035295 A035296

Keyword

easy,nonn

Author

Barry Brent (barryb(AT)primenet.com)

Status

approved