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A162321 Number of reduced words of length n in the Weyl group D_15. 1
1, 15, 119, 665, 2939, 10933, 35580, 103972, 277950, 689282, 1602727, 3523945, 7376794, 14784390, 28500705, 53054702, 95687240, 167682306, 286218490, 476893794, 777106448, 1240505775, 1942759458, 2988915740, 4522669833 (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 IV.)

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

LINKS

Table of n, a(n) for n=0..24.

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.

MATHEMATICA

n = 15;

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: A183475 A253804 A161476 * A161875 A259746 A139615

Adjacent sequences:  A162318 A162319 A162320 * A162322 A162323 A162324

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified November 26 07:49 EST 2020. Contains 338632 sequences. (Running on oeis4.)