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A109281
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Triangle T(n,k) of elements of n-th Weyl group of type B whose reduced word uses n-k generators.
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2
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1, 1, 1, 5, 2, 1, 35, 9, 3, 1, 309, 56, 14, 4, 1, 3287, 443, 84, 20, 5, 1, 41005, 4298, 623, 120, 27, 6, 1, 588487, 49937, 5629, 859, 165, 35, 7, 1, 9571125, 680700, 61300, 7360, 1162, 220, 44, 8, 1, 174230863, 10683103, 793402, 75714, 9584, 1544, 286, 54, 9, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums are 2^n n!; g.f. for k-th column is given by (1-1/g(x))^(k-1)*g(2x)/g(x)
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LINKS
| N. Bergeron, C. Hohlweg, M. Zabrocki, Posets related to the connectivity set of Coxeter groups
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FORMULA
| G.f.: g(2x)/(t+(1-t)g(x)) where g(x) = sum_{n>=0} n! x^n
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EXAMPLE
| T(3,1)=9 because B_3 is generated by {t,s1,s2} where t^2=s1^2=s2^2=(s1 s2)^3=(t s1)^4=(t s2)^2=1
The 9 elements which only use 2 generators are {s1 s2, s1 s2 s1, s2 s1, s2 t, t s1, s1 t s1, s1 t s1 t, s1 t, t s1 t}
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MAPLE
| f:=proc(n, k) local gx; gx:=add(i!*x^i, i=0..n); coeff(series((1-1/gx)^k*subs(x=2*x, gx)/gx, x, n+1), x, n); end:
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CROSSREFS
| Cf. A109253, A003319, A085771, A059438.
Sequence in context: A083801 A193590 A111544 * A133289 A107719 A174485
Adjacent sequences: A109278 A109279 A109280 * A109282 A109283 A109284
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KEYWORD
| nonn,tabl
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AUTHOR
| Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Aug 19 2005
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