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McKay-Thompson series of class 46C for the Monster group.
1

%I #17 Jun 28 2018 10:04:27

%S 1,0,2,1,3,3,5,5,10,8,14,14,23,21,33,32,49,49,69,70,99,100,136,142,

%T 190,198,259,271,351,370,469,498,627,665,824,884,1084,1162,1413,1518,

%U 1833,1974,2360,2548,3031,3272,3865,4185,4917,5321,6218,6739,7838

%N McKay-Thompson series of class 46C for the Monster group.

%C Also McKay-Thompson series of class 46D for the Monster group.

%H G. C. Greubel, <a href="/A058689/b058689.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>, Commun. 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 + 1 + 2/A, where A = eta(q)*eta(q^23)/(eta(q^2)* eta(q^46)), in powers of q. - _G. C. Greubel_, Jun 27 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n/23)) / (2^(3/4) * 23^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018

%e T46C = 1/q +2*q +q^2 +3*q^3 +3*q^4 +5*q^5 +5*q^6 +10*q^7 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q]*eta[q^23]/( eta[q^2]* eta[q^46])); a:= CoefficientList[Series[1 + A + 2/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 27 2018 *)

%o (PARI) q='q+O('q^50); A = eta(q)*eta(q^23)/(q*eta(q^2)* eta(q^46)); Vec(A + 1 + 2/A) \\ _G. C. Greubel_, Jun 27 2018

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

%K nonn

%O -1,3

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