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%I #19 Jul 02 2018 20:26:35
%S 1,0,1,1,1,0,1,1,2,1,2,1,3,2,3,3,4,3,5,4,6,5,7,6,9,7,11,9,13,11,15,13,
%T 18,16,21,19,25,22,29,27,34,31,40,37,46,43,53,50,62,58,71,68,83,78,95,
%U 91,109,104,124,120,143,137,162,158,185,180,210,206,239,234,270,266
%N McKay-Thompson series of class 104A for the Monster group.
%C Also McKay-Thompson series of class 104B for Monster. - _Michel Marcus_, Feb 19 2014
%H G. C. Greubel, <a href="/A112219/b112219.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>, Commun. 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 sqrt(T52A) in powers of q, where T52A = A058705. - _G. C. Greubel_, Jul 02 2018
%F a(n) ~ exp(sqrt(2*n/13)*Pi) / (2^(5/4) * 13^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018
%e T104A = 1/q +q^7 +q^11 +q^15 +q^23 +q^27 +2*q^31 +q^35 +2*q^39 +...
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= q^(1/2)*(eta[q^2]* eta[q^13]/(eta[q]*eta[q^26])); T52A:= B - q/B; a:= CoefficientList[ Series[(T52A + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jul 02 2018 *)
%o (PARI) q='q+O('q^70); B = (eta(q^2)*eta(q^13)/(eta(q)*eta(q^26))); Vec(sqrt(B - q/B)) \\ _G. C. Greubel_, Jul 02 2018
%K nonn
%O 0,9
%A _Michael Somos_, Aug 28 2005
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