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%I #10 Aug 26 2016 23:29:50
%S 1,4,9,15,20,22,20,15,9,4,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Number of reduced words of length n in the Weyl group A_4.
%C Computed with MAGMA using commands similar to those used to compute A161409.
%D N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche I.)
%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%F G.f. for A_m is the polynomial Product_{k=1..m}(1-x^(k+1))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A008302.
%t CoefficientList[Series[(1 - x^2) (1 - x^3) (1 - x^4) (1 - x^5) / (1 - x)^4, {x, 0, 20}], x] (* _Vincenzo Librandi_, Aug 23 2016 *)
%Y Cf. A008302, A161409.
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009
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