

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
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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..n1 )/ f(1)^n, where f(k) = 1x^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);
(1x^n) Product[1x^(2k), {k, 1, n1}]/(1x)^n // CoefficientList[#, y]& (* JeanFrançois 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



