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%I #13 Sep 08 2022 08:45:46
%S 1,8,35,112,294,672,1386,2640,4718,8000,12978,20272,30645,45016,64470,
%T 90264,123829,166768,220849,287992,370250,469784,588833,729680,894613,
%U 1085880,1305640,1555912,1838523,2155056,2506798,2894688,3319268,3780640,4278429
%N Number of reduced words of length n in the Weyl group E_8 on 8 generators and order 696729600.
%D N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche VII.)
%D H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.
%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%H Vincenzo Librandi, <a href="/A162494/b162494.txt">Table of n, a(n) for n = 0..120</a>
%F G.f.: (1-x^2)*(1-x^8)*(1-x^12)*(1-x^14)*(1-x^18)*(1-x^20)*(1-x^24)*(1-x^30)/(1-x)^8.
%t CoefficientList[Series[(1 - x^2) (1 - x^8) (1 - x^12) (1 - x^14) (1 - x^18) (1 - x^20) (1 - x^24) (1 - x^30) / (1 - x)^8, {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 09 2013 *)
%o (Magma) G := CoxeterGroup(GrpFPCox, "E8");
%o f := GrowthFunction(G);
%o Coefficients(f);
%o (PARI) Vec((1-x^2)*(1-x^8)*(1-x^12)*(1-x^14)*(1-x^18)*(1-x^20)*(1-x^24)*(1-x^30)/(1-x)^8 + O(x^121)) \\ _Jinyuan Wang_, Mar 08 2020
%Y Cf. A161409, A162493.
%K nonn,fini,full
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009
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