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A162365 Number of reduced words of length n in the Weyl group D_23. 1
1, 23, 275, 2277, 14673, 78407, 361514, 1477750, 5461235, 18518565, 58282576, 171815888, 477989151, 1262643305, 3183445871, 7694405993, 17895700206, 40182143330, 87349858045, 184297593435, 378236260170, 756560791350 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

Differs from A161930 first at index n=23. - R. J. Mathar, Jul 12 2010

REFERENCES

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

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.

LINKS

Table of n, a(n) for n=0..21.

FORMULA

G.f. for D_m is the polynomial f(n) * Product( f(2i), i=1..n-1 )/ f(1)^n, where f(k) = 1-x^k. Only finitely many terms are nonzero. This is a row of the triangle in A162206.

MAPLE

f := proc(n) 1-x^n ; end proc:

A162365 := proc(n) local m ; m := 23 ; f(m)*mul(f(2*i), i=1..m-1)/f(1)^m ; expand(%) ; coeftayl(%, x=0, n) ; end proc:

seq(A162365(n), n=0..23) ; # R. J. Mathar, Jul 12 2010

MATHEMATICA

n = 23;

x = y + y O[y]^(n^2);

(1-x^n) Product[1-x^(2k), {k, 1, n-1}]/(1-x)^n // CoefficientList[#, y]& (* Jean-François Alcover, Mar 25 2020, from A162206 *)

CROSSREFS

Sequence in context: A142027 A161523 A161930 * A162680 A010975 A022588

Adjacent sequences:  A162362 A162363 A162364 * A162366 A162367 A162368

KEYWORD

nonn

AUTHOR

John Cannon and N. J. A. Sloane, Dec 01 2009

STATUS

approved

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Last modified June 23 13:59 EDT 2021. Contains 345402 sequences. (Running on oeis4.)