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A162347 Number of reduced words of length n in the Weyl group D_19.

%I A162347 #13 Mar 17 2025 22:37:33
%S A162347 1,19,189,1311,7124,32300,127091,445721,1420364,4172476,11426240,
%T A162347 29429784,71808030,166970290,371826581,796341623,1646167391,
%U A162347 3294638285,6401307860,12102626403,22312161567,40184022241,70815180079,122291797486,207223385049,344958892116
%N A162347 Number of reduced words of length n in the Weyl group D_19.
%D A162347 N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.)
%D A162347 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%H A162347 Andrew Howroyd, <a href="/A162347/b162347.txt">Table of n, a(n) for n = 0..342</a>
%H A162347 <a href="/index/Gre#GROWTH">Index entries for growth series for groups</a>
%F A162347 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 A162347 # Growth series for D_k, truncated to terms of order M. - _N. J. A. Sloane_, Aug 07 2021
%p A162347 f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
%p A162347 g := proc(k,M) local a,i; global f;
%p A162347 a:=f(k)*mul(f(2*i),i=1..k-1);
%p A162347 seriestolist(series(a,x,M+1));
%p A162347 end proc;
%Y A162347 Row 19 of A162206.
%Y A162347 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.
%K A162347 nonn,fini,full
%O A162347 0,2
%A A162347 _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009