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

Author

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

Keywords

• nonn

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 alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

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.