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A161876 Number of reduced words of length n in the Weyl group B_16.

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%I A161876 #12 Mar 21 2025 21:56:50
%S A161876 1,16,135,800,3739,14672,50252,154224,432174,1121456,2724183,6248128,
%T A161876 13624922,28409312,56910017,109964720,205651975,373334400,659553555,
%U A161876 1136450288,1913567669,3154109024,5096972454,8086166144,12609525259,19348999600,29245158395,43578960064
%N A161876 Number of reduced words of length n in the Weyl group B_16.
%C A161876 Computed with MAGMA using commands similar to those used to compute A161409.
%D A161876 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%D A161876 N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)
%H A161876 Robert Israel, <a href="/A161876/b161876.txt">Table of n, a(n) for n = 0..256</a> (complete sequence)
%F A161876 G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.
%p A161876 G:= normal(mul((1-x^(2*k))/(1-x),k=1..16)):
%p A161876 seq(coeff(G,x,j),j=0..256); # _Robert Israel_, Mar 31 2017
%Y A161876 Row n=16 of A128084.
%K A161876 nonn,fini,full
%O A161876 0,2
%A A161876 _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009