login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058584 McKay-Thompson series of class 24a for Monster. 1

%I

%S 1,-5,-5,-9,-14,-19,-34,-55,-69,-104,-164,-209,-283,-413,-539,-712,

%T -968,-1248,-1642,-2167,-2731,-3526,-4592,-5736,-7244,-9255,-11520,

%U -14378,-18018,-22238,-27556,-34132,-41701,-51184,-62900,-76323,-92771,-113002,-136421,-164673,-198842,-238627

%N McKay-Thompson series of class 24a for Monster.

%H G. C. Greubel, <a href="/A058584/b058584.txt">Table of n, a(n) for n = -1..1000</a>

%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Comm. Algebra 22, No. 13, 5175-5193 (1994).

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F Expansion of A - 4*q/A, where A = q^(1/2)*(eta(q)*eta(q^3)/(eta(q^4)* eta(q^12))), in powers of q. - _G. C. Greubel_, Jun 21 2018

%F a(n) ~ -exp(sqrt(2*n/3)*Pi) / (2^(5/4) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2018

%e T24a = 1/q - 5*q - 5*q^3 - 9*q^5 - 14*q^7 - 19*q^9 - 34*q^11 - 55*q^13 - ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]*eta[q^3]/( eta[q^4]*eta[q^12])); a:= CoefficientList[Series[A - 4*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 21 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q)*eta(q^3)/(eta(q^4)* eta(q^12))); Vec(A - 4*q/A) \\ _G. C. Greubel_, Jun 21 2018

%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

%Y Cf. A058491.

%K sign

%O -1,2

%A _N. J. A. Sloane_, Nov 27 2000

%E Terms a(12) onward added by _G. C. Greubel_, Jun 21 2018

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)