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%I #14 Jun 28 2018 05:24:10
%S 1,-2,-2,-4,3,-2,-6,-4,7,-12,-10,-16,16,-14,-20,-20,29,-40,-40,-52,52,
%T -52,-70,-68,91,-114,-116,-148,149,-152,-190,-196,242,-296,-306,-368,
%U 383,-396,-478,-496,590,-698,-730,-856,897,-940,-1096,-1152,1342,-1548,-1630,-1876,1975,-2080,-2390,-2516
%N McKay-Thompson series of class 16f for the Monster group.
%H G. C. Greubel, <a href="/A112153/b112153.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(T8c - 4*q), where T8c = A112145, in powers of q.
%e T16f = 1/q - 2*q - 2*q^3 - 4*q^5 + 3*q^7 - 2*q^9 - 6*q^11 - 4*q^13 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= q^(1/2)*(eta[q]/ eta[q^2])^12; T4B := A + 64*q/A; T8c := Sqrt[(T4B /. {q -> q^4}) + O[q]^nmax]; a:= SeriesCoefficient[Sqrt[-4 *q + T8c + O[q]^nmax], {q, 0, n}]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 28 2018 *)
%K sign
%O 0,2
%A _Michael Somos_, Aug 28 2005
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