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McKay-Thompson series of class 24B for Monster.
2

%I #23 Jun 14 2018 20:25:10

%S 1,0,3,8,11,16,31,40,58,96,125,176,262,336,457,640,819,1088,1464,1864,

%T 2420,3168,3991,5088,6533,8160,10267,12976,16061,19968,24912,30576,

%U 37648,46464,56616,69136,84518,102288,123961,150304,180805,217664,262042,313472

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

%H G. C. Greubel, <a href="/A058572/b058572.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 a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4)*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Sep 07 2017

%F Expansion of -2 + (eta(q^2)*eta(q^4)*eta(q^6)*eta(q^12)/(eta(q)*eta(q^3) *eta(q^8)*eta(q^24)))^2 in powers of q. - _G. C. Greubel_, Jan 28 2018

%e T24B = 1/q + 3*q + 8*q^2 + 11*q^3 + 16*q^4 + 31*q^5 + 40*q^6 + 58*q^7 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[-2 + (eta[q^2]*eta[q^4]*eta[q^6]*eta[q^12]/(eta[q]*eta[q^3]*eta[q^8] *eta[q^24]))^2, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* _G. C. Greubel_, Jan 28 2018 *)

%o (PARI) q='q+O('q^50); A = -2 + (eta(q^2)*eta(q^4)*eta(q^6)*eta(q^12)/( eta(q)*eta(q^3)*eta(q^8)*eta(q^24)))^2/q; Vec(A) \\ _G. C. Greubel_, Jun 14 2018

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

%Y Cf. A212771 (same sequence except for n=0).

%K nonn

%O -1,3

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

%E More terms from _Michel Marcus_, Feb 18 2014