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A112147 McKay-Thompson series of class 12A for the Monster group. 2

%I #15 Jun 28 2018 04:49:17

%S 1,0,15,32,87,192,343,672,1290,2176,3705,6336,10214,16320,25905,39936,

%T 61227,92928,138160,204576,300756,435328,626727,897408,1271205,

%U 1790592,2508783,3487424,4824825,6641664,9083400,12371904,16778784

%N McKay-Thompson series of class 12A for the Monster group.

%H G. C. Greubel, <a href="/A112147/b112147.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 -6 + (eta(q^2)*eta(q^6))^12/((eta(q)*eta(q^3)*eta(q^4) *eta(q^12))^6) in powers of q. - _G. C. Greubel_, Jun 19 2018

%F a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018

%e T12A = 1/q + 15*q + 32*q^2 + 87*q^3 + 192*q^4 + 343*q^5 + 672*q^6 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[-6 + (eta[q^2]*eta[q^6])^12/((eta[q]*eta[q^3]*eta[q^4]*eta[q^12])^6), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 19 2018 *)

%o (PARI) q='q+O('q^50); A = -6 + (eta(q^2)*eta(q^6))^12/((eta(q)*eta(q^3) *eta(q^4)*eta(q^12))^6)/q; Vec(A) \\ _G. C. Greubel_, Jun 19 2018

%K nonn

%O -1,3

%A _Michael Somos_, Aug 28 2005

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)