%I #20 Jun 19 2018 12:32:32
%S 1,0,3,3,8,8,16,17,33,35,59,65,105,116,175,198,292,330,466,533,736,
%T 842,1132,1304,1725,1985,2576,2974,3809,4394,5555,6415,8030,9261,
%U 11475,13234,16264,18734,22843,26296,31849,36613,44058,50602,60551,69452,82669
%N McKay-Thompson series of class 30F for Monster.
%H G. C. Greubel, <a href="/A058617/b058617.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 a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 07 2017
%F Expansion of -1 + ((eta(q^3)*eta(q^5)*eta(q^6)*eta(q^10))/(eta(q)* eta(q^2)*eta(q^15)*eta(q^30))) in powers of q. - _G. C. Greubel_, Jun 18 2018
%e T30F = 1/q + 3*q + 3*q^2 + 8*q^3 + 8*q^4 + 16*q^5 + 17*q^6 + 33*q^7 + ...
%t nmax = 50; CoefficientList[Series[-x + Product[(1 - x^(3*k))*(1 - x^(5*k))*(1 - x^(6*k))*(1 - x^(10*k))/((1 - x^k)*(1 - x^(2*k))*(1 - x^(15*k))*(1 - x^(30*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 07 2017 *)
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= ((eta[q^3]*eta[q^5]*eta[q^6] *eta[q^10])/(eta[q]*eta[q^2]*eta[q^15]*eta[q^30])); a:= CoefficientList[Series[-1 + A, {q, 0, 60}], q]; Table[A058617[n], {n, 1, 50}] (* _G. C. Greubel_, Jun 18 2018 *)
%o (PARI) q='q+O('q^50); A = -1 + ((eta(q^3)*eta(q^5)*eta(q^6)*eta(q^10))/( eta(q)*eta(q^2)*eta(q^15)*eta(q^30)))/q; Vec(A) \\ _G. C. Greubel_, Jun 18 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A205977 (same sequence except for n=0).
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 18 2014