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A055106
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Triangle T(n,k) giving number of symmetric polynomials of degree n in k noncommuting variables, n >=2, 2 <= k <= n.
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9
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1, 1, 1, 1, 4, 1, 1, 12, 8, 1, 1, 33, 44, 13, 1, 1, 88, 208, 109, 19, 1, 1, 232, 910, 753, 223, 26, 1, 1, 609, 3809, 4674, 2091, 405, 34, 1, 1, 1596, 15521, 27161, 17220, 4926, 677, 43, 1, 1, 4180, 62185, 151134, 130480, 51702, 10342, 1064, 53, 1
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OFFSET
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2,5
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COMMENTS
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REFERENCES
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M. C. Wolf, Symmetric Functions of Non-commutative Elements, Duke Math. J., 2 (1936), 626-637.
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LINKS
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EXAMPLE
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T(1,1)=1 from Sum x_1; T(2,2)=1 from Sum x_1 x_2; T(3,2)=1 from Sum x_1 x_2 x_1; T(3,3)=1 from Sum x_1 x_2 x_3; ...
1; 1,1; 1,4,1; 1,12,8,1; 1,33,44,13,1; ...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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