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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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5
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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, 1197601448443963, 5950578465799856
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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 <=5
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LINKS
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FORMULA
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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
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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..30); # Alois P. Heinz, Sep 05 2008
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MATHEMATICA
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PROG
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(Magma) I:=[1, 1, 2, 6]; [n le 4 select I[n] else 10*Self(n-1)-32*Self(n-2)+37*Self(n-3)-11*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 09 2016
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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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