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%I #10 Jul 19 2015 10:35:22
%S 1,9,44,155,440,1068,2298,4489,8095,13640,21670,32683,47043,64889,
%T 86054,110010,135853,162337,187959,211089,230131,243694,250749,250749,
%U 243694,230131,211089,187959,162337,135853,110010,86054,64889,47043,32683,21670,13640,8095,4489,2298,1068,440,155,44,9,1
%N Number of reduced words of length n in the Weyl group A_9.
%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 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.
%t CoefficientList[Series[QFactorial[9+1,q],{q,0,9*(9+1)/2}],q] _Wouter Meeussen_, Jul 12 2014
%K fini,nonn,full
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009