A055106 Triangle T(n,k) giving number of symmetric polynomials of degree n in k noncommuting variables, n >=2, 2 <= k <= n.

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

Offset: 2

Author

N. J. A. Sloane, Jun 14 2000

Keywords

• nonn
• tabl
• nice

Comments

A055105 with first column deleted. - Sean A. Irvine, Mar 12 2022

Examples

			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; ...
		

References

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

Crossrefs

Row sums are A074664. Cf. A055105, A055107.

Extensions

More terms from Sean A. Irvine, Mar 12 2022