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McKay-Thompson series of class 94A for the Monster group.
1

%I #23 Jul 30 2018 00:37:40

%S 1,0,1,0,1,1,1,1,2,1,2,2,3,2,4,3,5,4,6,5,8,6,9,8,12,10,14,12,17,15,20,

%T 18,25,22,29,27,35,32,41,38,49,46,57,54,68,64,79,76,93,89,108,104,126,

%U 122,146,142,170,165,195,192,226,222,260,256,299,296,342

%N McKay-Thompson series of class 94A for the Monster group.

%C Also McKay-Thompson series of class 94B for Monster. - _Michel Marcus_, Feb 24 2014

%H Vaclav Kotesovec, <a href="/A058768/b058768.txt">Table of n, a(n) for n = -1..3200</a> (computed by David A. Madore)

%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 David A. Madore, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=1602206&amp;messageID=5836094">Coefficients of Moonshine (McKay-Thompson) series</a>, The Math Forum, Aug 01 2007.

%H David A. Madore, <a href="http://www.madore.org/~david/programs/#prog_moonshine">Computation of Moonshine Coefficients</a>

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

%F a(n) ~ exp(4*Pi*sqrt(n/94)) / (sqrt(2) * 94^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 10 2018

%e T94A = 1/q + q + q^3 + q^4 + q^5 + q^6 + 2*q^7 + q^8 + 2*q^9 + 2*q^10 + 3*q^11 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; Theta[a_, b_, c_] := Sum[q^((a*n^2 + b*n*m + c*m^2)/2), {n, -50, 50}, {m, -50, 50}]; T47A:= (Theta[2, 2, 24] - Theta[4, 2, 12])/(2*eta[q]*eta[q^47]); a:= CoefficientList[Series[ q*(T47A + (T47A /. {q -> q^2}) + T47A*(T47A /. {q -> q^2}))/(1 + T47A + (T47A /. {q -> q^2})), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 75}] (* _G. C. Greubel_, Jul 25 2018 *)

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

%K nonn

%O -1,9

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

%E More terms from _Michel Marcus_, Feb 24 2014