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

Author

N. J. A. Sloane, Jun 14 2000

Keywords

• nonn
• tabl
• nice

Comments

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

Examples

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

References

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

Crossrefs

Row sums are A074664. Cf. A055105, A055106.

Extensions

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