A161497 Number of reduced words of length n in the Weyl group A_17.

1, 17, 152, 951, 4674, 19210, 68646, 218995, 635682, 1703027, 4257634, 10020277, 22357907, 47572239, 96997223, 190297064, 360490592, 661386105, 1178290263, 2043049102, 3454679139, 5707038378, 9225153393, 14611938428, 22707091351

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.

Links

Robert Israel, Table of n, a(n) for n = 0..153 (complete sequence)

N. Bourbaki, Groupes et algèbres de Lie, Chap. 4, 5, 6. (The group is defined in Planche I.)

Formula

G.f. for A_m is the polynomial Product_{k=1..m}(1-x^(k+1))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A008302.

Maple

G:= normal(mul((1-x^(k+1))/(1-x), k=1..17)):
seq(coeff(G, x, j), j=0..17*18/2); # Robert Israel, Mar 28 2017

Crossrefs

Sequence in context: A299599 A244852 A064102 * A162328 A161877 A221737

Adjacent sequences: A161494 A161495 A161496 * A161498 A161499 A161500

Keyword

nonn,fini,full

Author

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

Status

approved