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 A162403 Number of reduced words of length n in the Weyl group D_41. 1
 1, 41, 860, 12300, 134889, 1209377, 9230207, 61657399, 367846424, 1990342376, 9885562358, 45508669878, 195729780567, 791712506207, 3028721321382, 11010682764150, 38197208930405, 126905454993645, 405078061871575 (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 N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche IV.) J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial. LINKS Robert Israel, Table of n, a(n) for n = 0..1640 FORMULA G.f. for D_m is the polynomial f(n) * Product( f(2i), i=1..n-1 )/ f(1)^n, where f(k) = 1-x^k. Only finitely many terms are nonzero. This is a row of the triangle in A162206. MAPLE f:= k -> 1-x^k: g:= n -> f(n)*mul(f(2*i), i=1..n-1)/f(1)^n: S:= expand(normal(g(41))): seq(coeff(S, x, j), j=0..degree(S, x)); # Robert Israel, Oct 07 2015 MATHEMATICA n = 41; x = y + y O[y]^(n^2); (1-x^n) Product[1-x^(2k), {k, 1, n-1}]/(1-x)^n // CoefficientList[#, y]& (* Jean-François Alcover, Mar 25 2020, from A162206 *) CROSSREFS Cf. A161409, A162206. Sequence in context: A299332 A161662 A162178 * A010993 A208431 A275355 Adjacent sequences:  A162400 A162401 A162402 * A162404 A162405 A162406 KEYWORD nonn,fini,full AUTHOR John Cannon and N. J. A. Sloane, Dec 01 2009 STATUS approved

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Last modified January 19 12:46 EST 2021. Contains 340269 sequences. (Running on oeis4.)