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A055106 Triangle T(n,k) giving number of symmetric polynomials of degree n in k noncommuting variables, n >=2, 2 <= k <= n. 9
1, 1, 1, 1, 4, 1, 1, 12, 8, 1, 1, 33, 44, 13, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,5

REFERENCES

M. C. Wolf, Symmetric Functions of Non-commutative Elements, Duke Math. J., 2 (1936), 626-637.

LINKS

Table of n, a(n) for n=2..16.

EXAMPLE

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; ...

CROSSREFS

Row sums are A074664. Cf. A055105, A055107.

Sequence in context: A192015 A205946 A101919 * A154372 A080416 A213166

Adjacent sequences:  A055103 A055104 A055105 * A055107 A055108 A055109

KEYWORD

nonn,tabl,nice

AUTHOR

N. J. A. Sloane, Jun 14 2000

STATUS

approved

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Last modified November 13 23:48 EST 2019. Contains 329106 sequences. (Running on oeis4.)