%I #16 Jun 29 2018 04:05:09
%S 1,0,1,1,1,2,2,3,3,3,4,6,7,8,9,10,12,14,17,19,21,24,29,33,38,43,48,54,
%T 61,70,79,88,98,111,124,140,157,174,193,214,239,266,295,326,361,398,
%U 441,488,538,592,650,715,786,864,948,1041,1138,1246,1364,1492
%N McKay-Thompson series of class 66B for Monster.
%H G. C. Greubel, <a href="/A058740/b058740.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>, Commun. Algebra 22, No. 13, 5175-5193 (1994).
%H David A. Madore, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&threadID=1602206&messageID=5836094">Coefficients of Moonshine (McKay-Thompson) series</a>, The Math Forum
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of -1 + A, where A = eta(q^2)*eta(q^3)*eta(q^22)*eta(q^33)/( eta(q)*eta(q^6)*eta(q^11)*eta(q^66)), in powers of q. - _G. C. Greubel_, Jun 29 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/33)) / (2^(3/4) * 33^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2018
%e T66B = 1/q + q + q^2 + q^3 + 2*q^4 + 2*q^5 + 3*q^6 + 3*q^7 + 3*q^8 + 4*q^9 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^2]*eta[q^3]*eta[q^22]* eta[q^33])/(eta[q]*eta[q^6]*eta[q^11]*eta[q^66]); a:= CoefficientList[Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 29 2018 *)
%o (PARI) q='q+O('q^50); A = eta(q^2)*eta(q^3)*eta(q^22)*eta(q^33)/( q*eta(q)*eta(q^6)*eta(q^11)*eta(q^66)); Vec(-1 + A) \\ _G. C. Greubel_, Jun 29 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,6
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 24 2014
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