A055107 Triangle T(k,n) giving number of symmetric polynomials of degree n in k noncommuting variables, n >=2, 2 <= k <= n.

1, 1, 1, 1, 4, 1, 1, 8, 12, 1, 1, 13, 44, 33, 1, 1, 19, 109, 208, 88, 1, 1, 26, 223, 753, 910, 232, 1, 1, 34, 405, 2091, 4674, 3809, 609, 1, 1, 43, 677, 4926, 17220, 27161, 15521, 1596, 1, 1, 53, 1064, 10342, 51702, 130480, 151134, 62185, 4180, 1

Offset

2,5

Comments

A055106 with rows reversed. - Sean A. Irvine, Mar 12 2022

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..56.

Example

1; 1,1; 1,4,1; 1,8,12,1; 1,13,44,33,1; ...

Crossrefs

Row sums are A074664. Cf. A055105, A055106.

Sequence in context: A317065 A316932 A317703 * A297193 A272867 A206438

Adjacent sequences: A055104 A055105 A055106 * A055108 A055109 A055110

Keyword

nonn,tabl,nice

Author

N. J. A. Sloane, Jun 14 2000

Extensions

More terms and offset corrected by Sean A. Irvine, Mar 12 2022

Status

approved