A161437 - OEIS

%I #10 Aug 26 2016 23:30:01

%S 1,5,14,29,49,71,90,101,101,90,71,49,29,14,5,1,0,0,0,0,0,0,0,0,0,0,0,

%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_5.

%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.

%t CoefficientList[Series[(1 - x^2) (1 - x^3) (1 - x^4) (1 - x^5) (1 - x^6) / (1 - x)^5, {x, 0, 120}], x] (* _Vincenzo Librandi_, Aug 23 2016 *)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009