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A124293
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Number of free generators of degree n of symmetric polynomials in 5-noncommuting variables.
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4
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1, 1, 2, 6, 22, 91, 406, 1896, 9093, 44279, 217500, 1073657, 5314870, 26352107, 130778039, 649352929, 3225196431, 16021584848, 79597062632, 395469296912, 1964908443531, 9762920818182, 48508934285620, 241027326818991
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Also the number of non-splitable set partitions (see Bergeron et al. reference) of length <=5
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REFERENCES
| N. Bergeron, C. Reutenauer, M. Rosas, M. Zabrocki, Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables, http://arXiv.org/abs/math.CO/0502082, to appear Canad. M. Journal
M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math. J. 2 (1936), 626-637.
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FORMULA
| O.g.f. (1-9q+24q^2-19q^3)/(1-10q+32q^2-37q^3+11q^4) = (1 - 1/(sum_{k=0}^5 q^k/(prod_{i=1}^k (1-i*q))))/q a(n) = add( A055105(n,k), k=1..5) = add(A055106(n,k),k=1..4)
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MAPLE
| a:= n-> (Matrix([[6, 2, 1, 1]]). Matrix(4, (i, j)-> if i=j-1 then 1 elif j=1 then [10, -32, 37, -11][i] else 0 fi)^(n-1))[1, 4]: seq (a(n), n=1..24); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 05 2008]
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CROSSREFS
| Cf. A055105, A055106, A055107, A074664, A001519, A124292, A124294, A124295.
Sequence in context: A089449 A150271 A150272 * A107591 A155866 A150273
Adjacent sequences: A124290 A124291 A124292 * A124294 A124295 A124296
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KEYWORD
| nonn
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AUTHOR
| Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24 2006
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