%I #7 Mar 12 2022 22:44:55

%S 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,

%T 232,1,1,34,405,2091,4674,3809,609,1,1,43,677,4926,17220,27161,15521,

%U 1596,1,1,53,1064,10342,51702,130480,151134,62185,4180,1

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

%C A055106 with rows reversed. - _Sean A. Irvine_, Mar 12 2022

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

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

%Y Row sums are A074664. Cf. A055105, A055106.

%K nonn,tabl,nice

%O 2,5

%A _N. J. A. Sloane_, Jun 14 2000

%E More terms and offset corrected by _Sean A. Irvine_, Mar 12 2022