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%I #12 Jul 02 2018 20:26:08
%S 1,0,1,-1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,-1,0,2,1,0,2,0,0,2,0,0,2,
%T -1,0,3,1,0,3,-1,0,4,1,0,5,0,0,5,0,0,5,-1,0,6,2,0,7,-2,0,8,2,0,9,-1,0,
%U 10,0,0,11,-1,0,12,3,0,14,-2,0,15,1,0,17,-1,0,18,1,0,20,-2,0,22,4,0,25,-5,0,28,3
%N McKay-Thompson series of class 90a for the Monster group.
%H G. C. Greubel, <a href="/A112214/b112214.txt">Table of n, a(n) for n = -1..1500</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^2/A, where A = q*(eta(q^3)*eta(q^18)*eta(q^30)* eta(q^45)/(eta(q^6)*eta(q^9)*eta(q^15)*eta(q^90))), in powers of q. - _G. C. Greubel_, Jul 02 2018
%e T90a = 1/q +q -q^2 +q^4 +q^7 +q^10 +q^13 +q^16 +q^19 -q^20 +...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q*(eta[q^3]*eta[q^18]*eta[q^30]* eta[q^45]/(eta[q^6]*eta[q^9]*eta[q^15]*eta[q^90])); T90a := A + q^2/A; a:= CoefficientList[Series[T90a, {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^3)*eta(q^18)*eta(q^30)* eta(q^45)/ (eta(q^6)*eta(q^9)*eta(q^15)*eta(q^90))); Vec(A + q^2/A) \\ _G. C. Greubel_, Jul 02 2018
%K sign
%O -1,24
%A _Michael Somos_, Aug 28 2005
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