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A161457 Number of reduced words of length n in the Weyl group A_9. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..45.

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 A050486

Adjacent sequences:  A161454 A161455 A161456 * A161458 A161459 A161460

KEYWORD

fini,nonn,full

AUTHOR

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

STATUS

approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)