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

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%I A055106 #7 Mar 12 2022 22:45:05
%S A055106 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 A055106 223,26,1,1,609,3809,4674,2091,405,34,1,1,1596,15521,27161,17220,4926,
%U A055106 677,43,1,1,4180,62185,151134,130480,51702,10342,1064,53,1
%N A055106 Triangle T(n,k) giving number of symmetric polynomials of degree n in k noncommuting variables, n >=2, 2 <= k <= n.
%C A055106 A055105 with first column deleted. - _Sean A. Irvine_, Mar 12 2022
%D A055106 M. C. Wolf, Symmetric Functions of Non-commutative Elements, Duke Math. J., 2 (1936), 626-637.
%e A055106 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 A055106 1; 1,1; 1,4,1; 1,12,8,1; 1,33,44,13,1; ...
%Y A055106 Row sums are A074664. Cf. A055105, A055107.
%K A055106 nonn,tabl,nice
%O A055106 2,5
%A A055106 _N. J. A. Sloane_, Jun 14 2000
%E A055106 More terms from _Sean A. Irvine_, Mar 12 2022