A162165 Number of reduced words of length n in the Weyl group B_37.

1, 37, 702, 9102, 90686, 740222, 5153693, 31465577, 171895451, 853189623, 3893872009, 16498746405, 65414952123, 244293496151, 864100862802, 2908662063474, 9355685557836, 28857543077604, 85625485744207

Offset

0,2

Comments

Computed with Magma using commands similar to those used to compute A161409.

References

N. Bourbaki, Groupes et algèbres 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

Table of n, a(n) for n=0..18.

Formula

G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.

Crossrefs

Sequence in context: A010953 A355600 A161650 * A162389 A010989 A103195

Adjacent sequences: A162162 A162163 A162164 * A162166 A162167 A162168

Keyword

nonn,more

Author

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

Status

approved