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A162327 Number of reduced words of length n in the Weyl group D_16.

%I A162327 #17 Mar 17 2025 17:20:56
%S A162327 1,16,135,800,3739,14672,50252,154224,432174,1121456,2724183,6248128,
%T A162327 13624922,28409312,56910017,109964720,205651974,373334384,659553420,
%U A162327 1136449488,1913563930,3154094352,5096922202,8086011920,12609093085,19347878144,29242434212,43572711936
%N A162327 Number of reduced words of length n in the Weyl group D_16.
%D A162327 N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.)
%D A162327 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%H A162327 Andrew Howroyd, <a href="/A162327/b162327.txt">Table of n, a(n) for n = 0..240</a>
%H A162327 <a href="/index/Gre#GROWTH">Index entries for growth series for groups</a>
%F A162327 The growth series for D_k is the polynomial f(k)*Prod_{i=1..k-1} f(2*i), where f(m) = (1-x^m)/(1-x) [Corrected by _N. J. A. Sloane_, Aug 07 2021]. This is a row of the triangle in A162206.
%p A162327 # Growth series for D_k, truncated to terms of order M. - _N. J. A. Sloane_, Aug 07 2021
%p A162327 f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
%p A162327 g := proc(k,M) local a,i; global f;
%p A162327 a:=f(k)*mul(f(2*i),i=1..k-1);
%p A162327 seriestolist(series(a,x,M+1));
%p A162327 end proc;
%Y A162327 Row 16 of A162206.
%Y A162327 Growth series for groups D_n, n = 3,...,50: A161435, A162207, A162208, A162209, A162210, A162211, A162212, A162248, A162288, A162297, A162300, A162301, A162321, 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.
%K A162327 nonn,fini,full
%O A162327 0,2
%A A162327 _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009