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A055107 Triangle T(k,n) giving number of symmetric polynomials of degree n in k noncommuting variables, n >=2, 2 <= k <= n.

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%I A055107 #7 Mar 12 2022 22:44:55
%S A055107 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 A055107 232,1,1,34,405,2091,4674,3809,609,1,1,43,677,4926,17220,27161,15521,
%U A055107 1596,1,1,53,1064,10342,51702,130480,151134,62185,4180,1
%N A055107 Triangle T(k,n) giving number of symmetric polynomials of degree n in k noncommuting variables, n >=2, 2 <= k <= n.
%C A055107 A055106 with rows reversed. - _Sean A. Irvine_, Mar 12 2022
%D A055107 M. C. Wolf, Symmetric Functions of Non-commutative Elements, Duke Math. J., 2 (1936), 626-637.
%e A055107 1; 1,1; 1,4,1; 1,8,12,1; 1,13,44,33,1; ...
%Y A055107 Row sums are A074664. Cf. A055105, A055106.
%K A055107 nonn,tabl,nice
%O A055107 2,5
%A A055107 _N. J. A. Sloane_, Jun 14 2000
%E A055107 More terms and offset corrected by _Sean A. Irvine_, Mar 12 2022