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Number of reduced words of length n in the Weyl group B_40.

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`%I #5 Jul 19 2015 10:22:21
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`%S 1,40,819,11440,122589,1074488,8020830,52427192,306189025,1622495952,
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`%T 7895219982,35623107520,150221110689,595982725640,2237008815175,
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`%U 7981961442768,27186526166255,88708246063240,278172606877930
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`%N Number of reduced words of length n in the Weyl group B_40.
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`%C Computed with MAGMA using commands similar to those used to compute A161409.
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`%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under PoincarĂ© polynomial.
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`%D N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)
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`%F G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.
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`%K nonn
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`%O 0,2
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`%A _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009
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