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A162359
Number of reduced words of length n in the Weyl group D_20.
50
1, 20, 209, 1520, 8644, 40944, 168035, 613756, 2034120, 6206596, 17632836, 47062620, 118870650, 285840940, 657667521, 1454009144, 3100176535, 6394814820, 12796122680, 24898749084, 47210910669, 87394933080
OFFSET
0,2
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.
FORMULA
The growth series for D_k is the polynomial f(k)*Prod_{i=1..k-1} f(2*i), where f(m) = (1-x^m)/(1-x) [Corrected by N. J. A. Sloane, Aug 07 2021]. This is a row of the triangle in A162206.
MAPLE
# Growth series for D_k, truncated to terms of order M. - N. J. A. Sloane, Aug 07 2021
f := proc(m::integer) (1-x^m)/(1-x) ; end proc:
g := proc(k, M) local a, i; global f;
a:=f(k)*mul(f(2*i), i=1..k-1);
seriestolist(series(a, x, M+1));
end proc;
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 01 2009
STATUS
approved