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%I A058616 #20 Jun 28 2018 03:44:58
%S A058616 1,2,3,6,9,12,18,26,34,48,66,86,115,152,196,252,324,410,518,652,815,
%T A058616 1016,1260,1556,1914,2344,2860,3482,4222,5104,6160,7408,8883,10634,
%U A058616 12694,15112,17962,21300,25198,29764,35091,41284,48495,56870,66567,77800,90790,105780,123070,142988
%N A058616 McKay-Thompson series of class 30E for Monster.
%H A058616 G. C. Greubel, <a href="/A058616/b058616.txt">Table of n, a(n) for n = -1..2500</a>
%H A058616 D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Comm. Algebra 22, No. 13, 5175-5193 (1994).
%H A058616 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A058616 Expansion of q^(1/3)*(eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^2 in powers of q. - _G. C. Greubel_, Jun 23 2018
%F A058616 a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018
%e A058616 T30E = 1/q + 2*q^2 + 3*q^5 + 6*q^8 + 9*q^11 + 12*q^14 + 18*q^17 + 26*q^20 + ...
%t A058616 eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/3)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 23 2018 *)
%o A058616 (PARI) q='q+O('q^50); Vec((eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^2) \\ _G. C. Greubel_, Jun 23 2018
%Y A058616 Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K A058616 nonn
%O A058616 -1,2
%A A058616 _N. J. A. Sloane_, Nov 27 2000
%E A058616 Terms a(8) onward added by _G. C. Greubel_, Jun 23 2018

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