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%I #27 Jun 02 2018 21:27:44
%S 1,2,15,-32,87,-192,343,-672,1290,-2176,3705,-6336,10214,-16320,25905,
%T -39936,61227,-92928,138160,-204576,300756,-435328,626727,-897408,
%U 1271205,-1790592,2508783,-3487424,4824825,-6641664,9083400,-12371904,16778784,-22630912,30407112,-40703040,54238342,-72018624,95300769
%N McKay-Thompson series of class 6C for Monster (and, apart from signs, of class 12A).
%C For n>0 same as A121666. - _Vaclav Kotesovec_, Apr 09 2016
%H G. C. Greubel, <a href="/A045486/b045486.txt">Table of n, a(n) for n = -1..1001</a>
%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%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 J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F a(n) ~ (-1)^(n+1) * exp(2*Pi*sqrt(n/3)) / (2*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Apr 09 2016
%F Expansion of 8 + (eta(q)*eta(q^3)/(eta(q^2)*eta(q^6)))^6. - _G. C. Greubel_, Jun 02 2018
%t nmax = 50; CoefficientList[Series[8*x + Product[((1-x^k)*(1-x^(3*k))/((1-x^(2*k))*(1-x^(6*k))))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 09 2016 *)
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q*(8 + (eta[q]*eta[q^3]/(eta[q^2]*eta[q^6]))^6), {q, 0, 60}], q]; Table[ a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 02 2018 *)
%o (PARI) N=66; q='q+O('q^N); Vec( ((eta(q^1)*eta(q^3))/(eta(q^2)*eta(q^6)))^6/q + 8 ) \\ _Joerg Arndt_, Apr 09 2016
%Y Cf. A007256.
%K sign
%O -1,2
%A _N. J. A. Sloane_
%E More terms from _Joerg Arndt_, Apr 09 2016
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