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%I #20 Jun 28 2018 10:48:49
%S 1,0,21,62,162,378,819,1680,3276,6138,11145,19662,33840,57048,94362,
%T 153432,245757,388218,605466,933414,1423614,2149586,3215844,4769544,
%U 7016572,10243896,14848809,21378276,30582360,43484304,61473438,86428896
%N McKay-Thompson series of class 10D for the Monster group.
%H G. C. Greubel, <a href="/A058100/b058100.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 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F G.f. is Fourier series of a weight 0 level 10 modular form. f(-1/ ( 10 t)) = f(t) where q = exp(2 Pi i t).
%F Expansion of -6 + ((eta(q^2)*eta(q^5))/(eta(q)*eta(q^10)))^6 in powers of q. - _G. C. Greubel_, May 05 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (2^(3/4) * 5^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e T10D = 1/q + 21*q + 62*q^2 + 162*q^3 + 378*q^4 + 819*q^5 + 1680*q^6 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[-6 + ((eta[q^2]*eta[q^5])/(eta[q]*eta[q^10]))^6, {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, May 05 2018 *)
%o (PARI) q='q+O('q^30); Vec(-6 + ((eta(q^2)*eta(q^5))/(eta(q)* eta(q^10)) )^6/q) \\ _G. C. Greubel_, May 05 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A132130(n) = a(n) unless n=0.
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 19 2014
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