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McKay-Thompson series of class 84a for Monster.
1

%I #22 Jul 10 2018 10:05:40

%S 1,-2,-1,-1,-1,-2,-1,-2,-2,-2,-2,-4,-3,-5,-4,-5,-5,-9,-6,-11,-9,-11,

%T -11,-16,-13,-21,-19,-22,-22,-31,-25,-38,-35,-42,-41,-53,-48,-66,-62,

%U -73,-75,-92,-84,-111,-107,-126,-127,-154,-145,-182,-180,-205,-211,-251,-242,-293,-291,-334

%N McKay-Thompson series of class 84a for Monster.

%H G. C. Greubel, <a href="/A058761/b058761.txt">Table of n, a(n) for n = -1..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 - q/A, where A = q^(1/2)*(eta(q)*eta(q^6)*eta(q^14)* eta(q^21)/(eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42))), in powers of q. - _G. C. Greubel_, Jun 30 2018

%F a(n) ~ -exp(2*Pi*sqrt(n/21)) / (2 * 21^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 10 2018

%e T84a = 1/q - 2*q - q^3 - q^5 - q^7 - 2*q^9 - q^11 - 2*q^13 - 2*q^15 - 2*q^17 - ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]*eta[q^6] *eta[q^14]*eta[q^21]/(eta[q^2]*eta[q^3]*eta[q^7]*eta[q^42])); a:= CoefficientList[Series[ Simplify[A - q/A, q>0] , {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 30 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q)*eta(q^6)*eta(q^14)* eta(q^21)/( eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42))); Vec(A - q/A) \\ _G. C. Greubel_, Jun 30 2018

%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

%K sign

%O -1,2

%A _N. J. A. Sloane_, Nov 27 2000

%E Terms a(12) onward added by _G. C. Greubel_, Jun 30 2018