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%I #20 Jul 20 2022 05:15:39
%S 1,0,1,1,1,0,3,2,2,2,2,2,5,3,6,5,7,5,10,7,11,11,13,12,19,15,21,22,26,
%T 23,35,30,39,38,47,45,60,54,68,69,81,78,104,95,117,118,137,134,171,
%U 162,192,197,225,223,274,265,313,318,363,363,434,424,494,508,570,575,675,670,765,789,884
%N McKay-Thompson series of class 84A for Monster.
%H G. C. Greubel, <a href="/A058758/b058758.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 B + q/B, where B = 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 02 2018
%e T84A = 1/q + q^3 + q^5 + q^7 + 3*q^11 + 2*q^13 + 2*q^15 + 2*q^17 + 2*q^19 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; B:= 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[B + q/B , {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 30 2018 *)
%o (PARI) q='q+O('q^50); B = (eta(q)*eta(q^6)*eta(q^14)*eta(q^21)/( eta(q^2) *eta(q^3)*eta(q^7)*eta(q^42))); Vec(B + q/B) \\ _G. C. Greubel_, Jun 30 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,7
%A _N. J. A. Sloane_, Nov 27 2000
%E Terms a(12) onward added by _G. C. Greubel_, Jun 30 2018
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