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%I #13 Jun 20 2018 03:20:28
%S 1,1,1,-1,2,-1,2,1,3,0,4,-1,5,1,7,0,8,0,10,1,13,-2,16,0,20,3,24,-2,30,
%T -2,36,4,43,0,52,-3,61,2,73,-1,86,-1,102,3,120,-4,140,-1,165,8,192,-5,
%U 224,-6,260,10,301,-2,348,-7,401,7,462,-2,530,-2,608,8,696,-10,796,-3,909,18,1035,-12
%N McKay-Thompson series of class 48a for the Monster group.
%H G. C. Greubel, <a href="/A112186/b112186.txt">Table of n, a(n) for n = 0..2500</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 + q/A, where A = q^(1/2)*(eta(q^6)*eta(q^8))/(eta(q^2) *eta(q^24)), in powers of q. - _G. C. Greubel_, Jun 19 2018
%e T48a = 1/q + q + q^3 - q^5 + 2*q^7 - q^9 + 2*q^11 + q^13 + 3*q^15 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^6]*eta[q^8])/(eta[q^2]*eta[q^24]); a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 30}] (* _G. C. Greubel_, Jun 19 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^8))/(eta(q^2) *eta(q^24)); Vec(A + q/A) \\ _G. C. Greubel_, Jun 19 2018
%K sign
%O 0,5
%A _Michael Somos_, Aug 28 2005
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