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 A161733 Number of reduced words of length n in the Weyl group B_9. 22
 1, 9, 44, 156, 449, 1113, 2463, 4983, 9372, 16588, 27886, 44846, 69387, 103763, 150538, 212538, 292779, 394371, 520399, 673783, 857121, 1072521, 1321430, 1604470, 1921291, 2270451, 2649332, 3054100, 3479715, 3919995, 4367735 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Computed with MAGMA using commands similar to those used to compute A161409. REFERENCES J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under PoincarĂ© polynomial. N. Bourbaki, Groupes et algĂ¨bres de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.) LINKS G. C. Greubel, Table of n, a(n) for n = 0..81 FORMULA G.f. for B_m is the polynomial Product_{k=1..m} (1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084. MAPLE seq(coeff(series(mul((1-x^(2k))/(1-x), k=1..9), x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 25 2018 MATHEMATICA 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)^9, {x, 0, 81}], x] (* Vincenzo Librandi, Aug 22 2016 *) PROG (PARI) t='t+O('t^40); Vec(prod(k=1, 9, 1-t^(2*k))/(1-t)^9) \\ G. C. Greubel, Oct 25 2018 (MAGMA) m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..9]])/(1-t)^9)); // G. C. Greubel, Oct 25 2018 CROSSREFS 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. Sequence in context: A075206 A161457 A162212 * A050486 A267176 A267171 Adjacent sequences:  A161730 A161731 A161732 * A161734 A161735 A161736 KEYWORD nonn,easy,fini,full AUTHOR John Cannon and N. J. A. Sloane, Nov 30 2009 STATUS approved

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)