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A112173 McKay-Thompson series of class 36b for the Monster group.

%I A112173 #19 Jun 16 2018 18:32:31
%S A112173 1,2,1,4,8,6,10,16,18,26,33,40,58,74,82,112,147,166,212,268,316,392,
%T A112173 476,560,695,838,967,1184,1430,1648,1970,2352,2731,3236,3803,4404,
%U A112173 5206,6080,6984,8192,9553,10942,12709,14736,16886,19506,22448,25648
%N A112173 McKay-Thompson series of class 36b for the Monster group.
%C A112173 Convolution square of A112206. - _Vaclav Kotesovec_, Sep 08 2015
%H A112173 G. C. Greubel, <a href="/A112173/b112173.txt">Table of n, a(n) for n = 0..1000</a>
%H A112173 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 A112173 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A112173 a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2015
%F A112173 Expansion of q^(1/3)*((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)*eta(q^4)* eta(q^12)))^2 in powers of q. - _G. C. Greubel_, Jun 16 2018
%F A112173 Expansion of abs(q^(1/3)*(eta(q)*eta(q^3)/(eta(q^2)*eta(q^6)))^2) in powers of q. - _G. C. Greubel_, Jun 16 2018
%e A112173 T36b = 1/q +2*q^2 +q^5 +4*q^8 +8*q^11 +6*q^14 +10*q^17 +...
%t A112173 nmax = 60; CoefficientList[Series[Product[((1 + x^k)*(1 + x^(3*k)) / ((1 + x^(2*k))*(1 + x^(6*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 08 2015 *)
%t A112173 eta[q_]:= q^(1/24)*QPochhammer[q];  a:= CoefficientList[Series[q^(1/3)*((eta[q^2]*eta[q^6])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^12]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 16 2018 *)
%o A112173 (PARI) q='q+O('q^50); A = ((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)* eta(q^4)*eta(q^12)))^2; Vec(A) \\ _G. C. Greubel_, Jun 16 2018
%Y A112173 Cf. A112206.
%K A112173 nonn
%O A112173 0,2
%A A112173 _Michael Somos_, Aug 28 2005