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Search: id:A124292
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| A124292 |
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Number of free generators of degree n of symmetric polynomials in 4-noncommuting variables. |
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+0
6
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| 1, 1, 2, 6, 21, 78, 297, 1143, 4419, 17118, 66366, 257391, 998406, 3873015, 15024609, 58285737, 226111986, 877174110, 3402893997, 13201132950, 51212274057, 198672129783, 770725711035, 2989941920334, 11599136512038, 44997518922327
(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 <=4
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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. (1-5q+5q^2)/(1-6q+9q^2-3q^3) = 1 - 1/(sum_{k=0}^4 q^k/(prod_{i=1}^k (1-i*q))) a(n) = A055105(n,1)+A055105(n,2)+A055105(n,3)+A055105(n,4) = A055106(n,1)+A055106(n,2)+A055106(n,3)
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MAPLE
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a:= n-> (Matrix([[2, 1, 1]]). Matrix(3, (i, j)-> if i=j-1 then 1 elif j=1 then [6, -9, 3][i] else 0 fi)^(n-1))[1, 3]: seq (a(n), n=1..26); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 05 2008]
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CROSSREFS
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Cf. A055105, A055106, A055107, A074664, A001519, A124293, A124294, A124295.
Sequence in context: A150188 A150189 A144169 this_sequence A129776 A129775 A054515
Adjacent sequences: A124289 A124290 A124291 this_sequence A124293 A124294 A124295
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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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