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 A161716 Number of reduced words of length n in the Weyl group B_7. 22
 1, 7, 27, 77, 181, 371, 686, 1170, 1869, 2827, 4082, 5662, 7581, 9835, 12399, 15225, 18242, 21358, 24464, 27440, 30162, 32510, 34376, 35672, 36336, 36336, 35672, 34376, 32510, 30162, 27440, 24464, 21358, 18242, 15225, 12399, 9835, 7581, 5662 (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 Poincaré polynomial. N. Bourbaki, Groupes et algèbres 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..49 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..7), x, n+1), x, n), n = 0 .. 40); # 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)^7, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 22 2016 *) PROG (PARI) t='t+O('t^50); Vec(prod(k=1, 7, 1-t^(2*k))/(1-t)^7) \\ G. C. Greubel, Oct 25 2018 (MAGMA) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..7]])/(1-t)^7)); // 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: A161439 A039623 A162210 * A162493 A005585 A161410 Adjacent sequences:  A161713 A161714 A161715 * A161717 A161718 A161719 KEYWORD nonn,easy,fini,full AUTHOR John Cannon and N. J. A. Sloane, Nov 30 2009 STATUS approved

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Last modified July 14 03:42 EDT 2020. Contains 335716 sequences. (Running on oeis4.)