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Search: id:A124294
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| A124294 |
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Number of free generators of degree n of symmetric polynomials in 6-noncommuting variables. |
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+0
5
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| 1, 1, 2, 6, 22, 92, 425, 2119, 11184, 61499, 347980, 2007643, 11734604, 69181578, 410179429, 2441025998, 14562284120, 87012222100, 520458020949, 3115224471290, 18654716694895, 111741999352603, 669466118302169
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Also the number of non-splitable set partitions (see Bergeron et. al. reference) of length <=6
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REFERENCES
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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
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O.g.f. (1-14*q+68*q^2-135*q^3+91*q^4)/(1-15*q+81*q^2-192*q^3+189*q^4-53*q^5) = (1 - 1/(sum_{k=0}^6 q^k/(prod_{i=1}^k (1-i*q))))/q a(n) = add( A055105(n,k), k=1..6) = add(A055106(n,k),k=1..5)
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CROSSREFS
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Cf. A055105, A055106, A055107, A074664, A001519, A124292, A124293, A124295.
Sequence in context: A130579 A107945 A014330 this_sequence A124295 A074664 A091768
Adjacent sequences: A124291 A124292 A124293 this_sequence A124295 A124296 A124297
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KEYWORD
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nonn
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AUTHOR
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Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24 2006
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