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%I #15 Jul 03 2018 13:45:02
%S 1,-1,-1,0,0,0,0,-1,0,-1,0,-1,-1,0,0,1,0,-1,0,-1,1,-1,-2,0,-1,1,-1,-1,
%T 0,-1,2,-2,-3,0,0,1,-1,-3,0,-2,2,-3,-4,0,-1,3,-2,-4,0,-2,3,-4,-6,0,-2,
%U 3,-3,-5,0,-3,6,-6,-9,0,-2,4,-4,-9,0,-5,6,-8,-11,0,-3,8,-6,-12,0,-6,9,-10,-16,0,-6,9,-9,-15,0,-8,14,-15,-22,0,-6,12,-11
%N McKay-Thompson series of class 60d for the Monster group.
%H G. C. Greubel, <a href="/A112202/b112202.txt">Table of n, a(n) for n = 0..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 sqrt((-8 - T15b(q) - T15b(q^2) + T15b(q)*T15b(q^2))/(5 + T15b(q) + T15b(q^2))) in powers of q, where T15b(q) = A058513. - _G. C. Greubel_, Jul 02 2018
%e T60d = 1/q -q -q^3 -q^13 -q^17 -q^21 -q^23 +q^29 -q^33 -q^37 +...
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q]/eta[q^25]); d:= q*(eta[q^3]/eta[q^15])^2; c:= (eta[q^3]*eta[q^5]/(eta[q]* eta[q^15]))^3; T25A := B + 5/B; A:= (eta[q^3]/eta[q^75]); T15b:= Simplify[2 + (-5 + T25A*(A + 5/A))*(-B + A)*(1/(A*B))^2*(d^3/c)/q^3, q>0]; T60d:= CoefficientList[Series[(q*((-8 - T15b - (T15b /. {q -> q^2}) + T15b*(T15b /. {q -> q^2}))/(5 + T15b + (T15b /. {q -> q^2}))) + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[T60d[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jul 02 2018 *)
%K sign
%O 0,23
%A _Michael Somos_, Aug 28 2005
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