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%I #17 Jul 03 2018 03:57:53
%S 1,-1,0,1,1,1,0,0,1,0,1,-1,0,1,1,2,-2,0,1,1,3,-1,0,2,1,3,-2,0,2,1,5,
%T -4,0,4,3,6,-3,0,4,2,7,-5,0,5,4,10,-7,0,7,5,12,-7,0,9,5,14,-9,0,10,6,
%U 20,-14,0,14,10,23,-13,0,16,9,27,-18,0,19,13,35,-24,0,24,16,42,-25,0,29,18,48,-31,0,33
%N McKay-Thompson series of class 45c for the Monster group.
%H G. C. Greubel, <a href="/A112185/b112185.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 (T15b - 3)^(1/3), where T15b = A058513. - _G. C. Greubel_, Jun 30 2018
%e T45c = 1/q - q^2 + q^8 + q^11 + q^14 + q^23 + q^29 - q^32 + q^38 + q^41 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q]/eta[q^25]); d:= q*(eta[q^3]/eta[q^15])^2; c:= (eta[q^3]*eta[q^5]/(eta[q]* eta[q^15]))^3; T25A := B + 5/B; A:= (eta[q^3]/eta[q^75]); T15b:= 2 + (-5 + T25A*(A + 5/A))*(-B + A)*(1/(A*B))^2*(d^3/c)/q^3; a:= CoefficientList[ Series[(q*(T15b - 3) + O[q]^nmax)^(1/3), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jun 30 2018, fixed by _Vaclav Kotesovec_, Jul 03 2018 *)
%K sign
%O 0,16
%A _Michael Somos_, Aug 28 2005
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