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A162461 Number of reduced words of length n in the Weyl group D_48.

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%I A162461 #7 Feb 21 2024 11:53:23
%S A162461 1,48,1175,19552,248723,2579312,22706404,174482000,1194358970,
%T A162461 7396268880,41942496051,219939217728,1075086490926,4931595192160,
%U A162461 21350092231441,87658196804688,342762976614961,1281150739056160
%N A162461 Number of reduced words of length n in the Weyl group D_48.
%C A162461 Computed with MAGMA using commands similar to those used to compute A161409.
%D A162461 N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.)
%D A162461 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%H A162461 <a href="/index/Gre#GROWTH">Index entries for growth series for groups</a>
%F A162461 G.f. for D_m is the polynomial f(n) * Product( f(2i), i=1..n-1 )/ f(1)^n, where f(k) = 1-x^k. Only finitely many terms are nonzero. This is a row of the triangle in A162206.
%Y A162461 Growth series for groups D_n, n = 3,...,50: A161435, A162207, A162208, A162209, A162210, A162211, A162212, A162248, A162288, A162297, A162300, A162301, A162321, A162327, A162328, A162346, A162347, A162359, A162360, A162364, A162365, A162366, A162367, A162368, A162369, A162370, A162376, A162377, A162378, A162379, A162380, A162381, A162384, A162388, A162389, A162392, A162399, A162402, A162403, A162411, A162412, A162413, A162418, A162452, A162456, A162461, A162469, A162492; also A162206.
%K A162461 nonn
%O A162461 0,2
%A A162461 _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009