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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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4
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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
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OFFSET
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1,3
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COMMENTS
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Also the number of non-splitable set partitions (see Bergeron et al. reference) of length <=6
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LINKS
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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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MATHEMATICA
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LinearRecurrence[{15, -81, 192, -189, 53}, {1, 1, 2, 6, 22}, 23] (* Jean-François Alcover, Dec 04 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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