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A162403 Number of reduced words of length n in the Weyl group D_41. 1
1, 41, 860, 12300, 134889, 1209377, 9230207, 61657399, 367846424, 1990342376, 9885562358, 45508669878, 195729780567, 791712506207, 3028721321382, 11010682764150, 38197208930405, 126905454993645, 405078061871575 (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

Robert Israel, Table of n, a(n) for n = 0..1640

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:= k -> 1-x^k:

g:= n -> f(n)*mul(f(2*i), i=1..n-1)/f(1)^n:

S:= expand(normal(g(41))):

seq(coeff(S, x, j), j=0..degree(S, x)); # Robert Israel, Oct 07 2015

CROSSREFS

Cf. A161409, A162206.

Sequence in context: A010957 A161662 A162178 * A010993 A208431 A275355

Adjacent sequences:  A162400 A162401 A162402 * A162404 A162405 A162406

KEYWORD

nonn,fini,full

AUTHOR

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

STATUS

approved

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Last modified August 18 14:32 EDT 2017. Contains 290720 sequences.