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A161457
Number of reduced words of length n in the Weyl group A_9.
1
1, 9, 44, 155, 440, 1068, 2298, 4489, 8095, 13640, 21670, 32683, 47043, 64889, 86054, 110010, 135853, 162337, 187959, 211089, 230131, 243694, 250749, 250749, 243694, 230131, 211089, 187959, 162337, 135853, 110010, 86054, 64889, 47043, 32683, 21670, 13640, 8095, 4489, 2298, 1068, 440, 155, 44, 9, 1
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 I.)
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
FORMULA
G.f. for A_m is the polynomial Prod_{k=1..m}(1-x^(k+1))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A008302.
MATHEMATICA
CoefficientList[Series[QFactorial[9+1, q], {q, 0, 9*(9+1)/2}], q] Wouter Meeussen, Jul 12 2014
CROSSREFS
Sequence in context: A223647 A034194 A075206 * A162212 A161733 A374931
KEYWORD
fini,nonn,full
AUTHOR
John Cannon and N. J. A. Sloane, Nov 30 2009
STATUS
approved