%I A124295
%S A124295 1,1,2,6,22,92,426,2145,11589,66425,399682,2500037,16115347,106266473,
%T A124295 712602272,4837372576,33128183406,228308233098,1580495251012,
%U A124295 10976092266889,76398165848091,532614662149795,3717370694711130
%N A124295 Number of free generators of degree n of symmetric polynomials in 7-noncommuting 
               variables.
%C A124295 Also the number of non-splitable set partitions (see Bergeron et. al. 
               reference) of length <=7
%D A124295 N. Bergeron, C. Reutenauer, M. Rosas, M. Zabrocki, Invariants and Coinvariants 
               of the Symmetric Group in Noncommuting Variables, http://arXiv.org/
               abs/math.CO/0502082, to appear Canad. M. Journal
%D A124295 M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math. 
               J. 2 (1936), 626-637.
%F A124295 O.g.f. (1-20*q+151*q^2-535*q^3+881*q^4-531*q^5)/(1-21*q+170*q^2-669*q^3+1314*q^4-1157*q^5+309*q^6) 
               = (1 - 1/(sum_{k=0}^7 q^k/(prod_{i=1}^k (1-i*q))))/q a(n) = add( 
               A055105(n,k), k=1..7) = add(A055106(n,k),k=1..6)
%Y A124295 Cf. A055105, A055106, A055107, A074664, A001519, A124292, A124293, A124294.
%Y A124295 Sequence in context: A107945 A014330 A124294 this_sequence A074664 A091768 
               A150274
%Y A124295 Adjacent sequences: A124292 A124293 A124294 this_sequence A124296 A124297 
               A124298
%K A124295 nonn
%O A124295 1,3
%A A124295 Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24 2006