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A161878 Number of reduced words of length n in the Weyl group B_18.

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%I A161878 #9 Mar 17 2025 18:32:35
%S A161878 1,18,170,1122,5813,25176,94791,318630,974643,2752112,7253764,
%T A161878 18003544,42378246,95162260,204856291,424515042,849825768,1648470894,
%U A161878 3106669575,5701318544,10209535182,17871860844,30631158960,51476623220,84931612739
%N A161878 Number of reduced words of length n in the Weyl group B_18.
%C A161878 Computed with MAGMA using commands similar to those used to compute A161409.
%D A161878 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%D A161878 N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)
%H A161878 Andrew Howroyd, <a href="/A161878/b161878.txt">Table of n, a(n) for n = 0..324</a>
%F A161878 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.
%Y A161878 Row n=18 of A128084.
%K A161878 nonn,fini,full
%O A161878 0,2
%A A161878 _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009