A055106 - OEIS

%I #7 Mar 12 2022 22:45:05

%S 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,

%T 223,26,1,1,609,3809,4674,2091,405,34,1,1,1596,15521,27161,17220,4926,

%U 677,43,1,1,4180,62185,151134,130480,51702,10342,1064,53,1

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

%C A055105 with first column deleted. - _Sean A. Irvine_, Mar 12 2022

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

%e 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; ...

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

%Y Row sums are A074664. Cf. A055105, A055107.

%K nonn,tabl,nice

%O 2,5

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

%E More terms from _Sean A. Irvine_, Mar 12 2022