A161875 Number of reduced words of length n in the Weyl group B_15.

1, 15, 119, 665, 2939, 10933, 35580, 103972, 277950, 689282, 1602727, 3523945, 7376794, 14784390, 28500705, 53054703, 95687255, 167682425, 286219155, 476896733, 777117381, 1240541355, 1942863430, 2989193690, 4523359115, 6739474341, 9896158795, 14333801669, 20495294280

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 II.)

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..225

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

G:= normal(mul((1-x^(2*k))/(1-x), k=1..15)):
seq(coeff(G, x, j), j=0..15^2); # Robert Israel, Nov 26 2017

Crossrefs

Row n=15 of A128084.

Sequence in context: A253804 A161476 A162321 * A259746 A139615 A196506

Adjacent sequences: A161872 A161873 A161874 * A161876 A161877 A161878

Keyword

nonn,fini,full

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Extensions

a(28) corrected by Sean A. Irvine, Mar 23 2025

Status

approved