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A161733
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Number of reduced words of length n in the Weyl group B_9.
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22
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1, 9, 44, 156, 449, 1113, 2463, 4983, 9372, 16588, 27886, 44846, 69387, 103763, 150538, 212538, 292779, 394371, 520399, 673783, 857121, 1072521, 1321430, 1604470, 1921291, 2270451, 2649332, 3054100, 3479715, 3919995, 4367735
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OFFSET
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0,2
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COMMENTS
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Computed with MAGMA using commands similar to those used to compute A161409.
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REFERENCES
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J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
N. Bourbaki, Groupes et algèbres de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)
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LINKS
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FORMULA
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G.f. for B_m is the polynomial Product_{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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MAPLE
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seq(coeff(series(mul((1-x^(2k))/(1-x), k=1..9), x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 25 2018
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MATHEMATICA
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CoefficientList[Series[(1 - x^2) (1 -x^4) (1 - x^6) (1 - x^8) (1 - x^10) (1 - x^12) (1 - x^14) (1 - x^16) (1 - x^18) / (1 - x)^9, {x, 0, 81}], x] (* Vincenzo Librandi, Aug 22 2016 *)
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PROG
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(PARI) t='t+O('t^40); Vec(prod(k=1, 9, 1-t^(2*k))/(1-t)^9) \\ G. C. Greubel, Oct 25 2018
(Magma) m:=40; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..9]])/(1-t)^9)); // G. C. Greubel, Oct 25 2018
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CROSSREFS
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KEYWORD
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nonn,easy,fini,full
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AUTHOR
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STATUS
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approved
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