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A161776 Number of reduced words of length n in the Weyl group B_11.

%I A161776 #24 Sep 08 2022 08:45:45
%S A161776 1,11,65,275,934,2706,6941,16159,34749,69927,132991,240901,418198,
%T A161776 699258,1130856,1774992,2711907,4043193,5894878,8420346,11802934,
%U A161776 16258034,22034519,29415309,38716897,50287667,64504857,81770051
%N A161776 Number of reduced words of length n in the Weyl group B_11.
%C A161776 Computed with MAGMA using commands similar to those used to compute A161409.
%D A161776 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%D A161776 N. Bourbaki, Groupes et algèbres de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)
%H A161776 G. C. Greubel, <a href="/A161776/b161776.txt">Table of n, a(n) for n = 0..121</a>
%F A161776 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.
%p A161776 seq(coeff(series(mul((1-x^(2*k))/(1-x),k=1..11),x,122), x, n), n = 0 .. 121); # _Muniru A Asiru_, Oct 25 2018
%t A161776 CoefficientList[Series[((1 - x^2) (1 - x^4) (1 - x^6) (1 - x^8) (1 - x^10) (1 - x^12) (1 - x^14) (1 - x^16) (1 - x^18) (1 - x^20) (1 - x^22)) / (1 - x)^11, {x, 0, 121}], x] (* _Vincenzo Librandi_, Aug 22 2016 *)
%o A161776 (PARI) t='t+O('t^40); Vec(prod(k=1,11,1-t^(2*k))/(1-t)^11) \\ _G. C. Greubel_, Oct 24 2018
%o A161776 (Magma) m:=40; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..11]])/(1-t)^11)); // _G. C. Greubel_, Oct 24 2018
%Y A161776 The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696-A161699, A161716, A161717, A161733, A161755, A161776, A161858. These are all rows of A128084. The growth series for the affine Coxeter (or Weyl) groups B_2 through B_12 are A008576, A008137, A267167-A267175.
%K A161776 nonn,easy,fini,full
%O A161776 0,2
%A A161776 _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009