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A035293 Fourier coefficients of T_6. 3

%I #13 Oct 04 2020 07:19:16

%S 1,504,73764,2695040,54755730,778640256,8638286840,79534711296,

%T 632179869615,4456706505600,28415446027380,166276832866560,

%U 903193785328974,4595374951395840,22061107725128280,100534965940777984

%N Fourier coefficients of T_6.

%C T_6 is the unique weight = -4 normalized meromorphic modular form for SL(2,Z) with all poles at infinity.

%D C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980, pp. 249-268.

%H Seiichi Manyama, <a href="/A035293/b035293.txt">Table of n, a(n) for n = -1..1000</a>

%F G.f.: G_8/Delta (in Siegel's notation).

%F G.f.: E_4^2 / Delta where Delta = eta(q)^24. - _Sean A. Irvine_, Oct 03 2020

%F a(n) ~ exp(4*Pi*sqrt(n)) / (sqrt(2) * n^(11/4)). - _Vaclav Kotesovec_, Oct 04 2020

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

%Y Cf. A004009, A035281.

%K easy,nonn

%O -1,2

%A Barry Brent (barryb(AT)primenet.com)

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Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)