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A162377 Number of reduced words of length n in the Weyl group D_30.

%I A162377 #17 Mar 17 2025 22:36:37
%S A162377 1,30,464,4930,40454,273266,1581775,8064464,36943940,154385704,
%T A162377 595514217,2140442150,7224301969,23043923160,69844600965,202081362622,
%U A162377 560350431315,1494273031164,3843681391300,9562404542460,23062890166272,54038223288580,123239023118274,274026717741240
%N A162377 Number of reduced words of length n in the Weyl group D_30.
%D A162377 N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.)
%D A162377 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%H A162377 Andrew Howroyd, <a href="/A162377/b162377.txt">Table of n, a(n) for n = 0..870</a>
%H A162377 <a href="/index/Gre#GROWTH">Index entries for growth series for groups</a>
%F A162377 The growth series for D_k is the polynomial f(k)*Product_{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 A162377 # Growth series for D_k, truncated to terms of order M. - _N. J. A. Sloane_, Aug 07 2021
%p A162377 f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
%p A162377 g := proc(k,M) local a,i; global f;
%p A162377 a:=f(k)*mul(f(2*i),i=1..k-1);
%p A162377 seriestolist(series(a,x,M+1));
%p A162377 end proc;
%t A162377 f[m_] := (1-x^m)/(1-x);
%t A162377 With[{k = 30}, CoefficientList[f[k]*Product[f[2i], {i, 1, k-1}] + O[x]^(k-9), x]] (* _Jean-François Alcover_, Feb 15 2023, after Maple code *)
%Y A162377 Row 30 of A162206.
%Y A162377 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 A162377 nonn,fini,full
%O A162377 0,2
%A A162377 _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009