%I #22 Jun 15 2018 09:27:27
%S 1,0,-1,1,0,1,2,0,1,2,0,-1,4,0,1,4,0,-1,6,0,-1,7,0,2,11,0,0,12,0,-2,
%T 16,0,0,19,0,1,25,0,-1,29,0,2,37,0,1,44,0,-5,56,0,3,65,0,2,80,0,-5,94,
%U 0,4,114,0,-1,133,0,-4,160,0,7,187,0,0,223,0,-6,258,0,3,305,0,3,353,0,-6,415,0
%N McKay-Thompson series of class 45a for Monster.
%D D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
%H G. A. Edgar, <a href="/A058685/b058685.txt">Table of n, a(n) for n = -1..1000</a>
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of eta(q^9)*eta(q^15) / (eta(q^3)*eta(q^45)) - eta(q^3)*eta(q^45) / (eta(q^9)*eta(q^15)) in powers of q. - _G. A. Edgar_, Mar 20 2017
%e T45a = 1/q - q + q^2 + q^4 + 2*q^5 + q^7 + 2*q^8 - q^10 + 4*q^11 + q^13 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q*eta[q^9]*eta[q^15]/(eta[q^3] *eta[q^45]); a := CoefficientList[Series[A - q^2/A , {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 14 2018 *)
%o (PARI) q='q+O('q^99); Vec(eta(q^9)*eta(q^15) / (eta(q^3)*eta(q^45)) - q^2 * eta(q^3)*eta(q^45) / (eta(q^9)*eta(q^15))) \\ _Joerg Arndt_, Mar 20 2017
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K sign
%O -1,7
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _G. A. Edgar_, Mar 20 2017