%I #11 Jul 02 2018 14:20:13
%S 1,-1,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,2,1,0,0,
%T 0,0,2,-1,0,0,0,0,3,1,0,0,0,0,3,-1,0,0,0,0,3,0,0,0,0,0,4,0,0,0,0,0,5,
%U 1,0,0,0,0,6,-2,0,0,0,0,7,2,0,0,0,0,8,-1,0,0,0,0,9,0,0,0,0,0,10,-1,0,0,0,0
%N McKay-Thompson series of class 72c for the Monster group.
%H G. C. Greubel, <a href="/A112207/b112207.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^12)*eta(q^18)/(eta(q^6)* eta(q^36))), in powers of q. - _G. C. Greubel_, Jul 02 2018
%e T72c = 1/q -q +q^11 +q^13 +q^23 +q^35 +q^47 +2*q^59 +q^61 +...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^12]*eta[q^18]/(eta[q^6]*eta[q^36])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jul 02 2018 *)
%o (PARI) q='q+O('q^80); A = (eta(q^12)*eta(q^18)/(eta(q^6)* eta(q^36))); Vec(A - q/A) \\ _G. C. Greubel_, Jul 02 2018
%K sign
%O 0,31
%A _Michael Somos_, Aug 28 2005