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%I #12 Jun 28 2018 02:49:25
%S 1,-2,2,4,3,-2,6,4,7,-12,10,16,16,-14,20,20,29,-40,40,52,52,-52,70,68,
%T 91,-114,116,148,149,-152,190,196,242,-296,306,368,383,-396,478,496,
%U 590,-698,730,856,897,-940,1096,1152,1342,-1548,1630,1876,1975,-2080,2390,2516
%N McKay-Thompson series of class 16h for the Monster group.
%H G. C. Greubel, <a href="/A112155/b112155.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 A - 2*q/A, where A = q^(1/2)*(eta(q^4)*eta(q^8)/(eta(q^2)* eta(q^16)))^2, in powers of q. - _G. C. Greubel_, Jun 28 2018
%e T16h = 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]; A:= q^(1/2)*(eta[q^4]*eta[q^8]/( eta[q^2]*eta[q^16]))^2; a:= CoefficientList[Series[A - 2*q/A, {q, 0, n}]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 28 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^4)*eta(q^8)/(eta(q^2)* eta(q^16)))^2; Vec(A - 2*q/A) \\ _G. C. Greubel_, Jun 28 2018
%K sign
%O 0,2
%A _Michael Somos_, Aug 28 2005