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%I #5 Jul 19 2015 10:35:30
%S 1,8,35,111,285,628,1230,2191,3606,5545,8031,11021,14395,17957,21450,
%T 24584,27073,28675,29228,28675,27073,24584,21450,17957,14395,11021,
%U 8031,5545,3606,2191,1230,628,285,111,35,8,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Number of reduced words of length n in the Weyl group A_8.
%C Computed with MAGMA using commands similar to those used to compute A161409.
%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%D N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche I.)
%F G.f. for A_m is the polynomial Prod_{k=1..m}(1-x^(k+1))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A008302.
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009
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