%I A124294
%S A124294 1,1,2,6,22,92,425,2119,11184,61499,347980,2007643,11734604,69181578,
%T A124294 410179429,2441025998,14562284120,87012222100,520458020949,
%U A124294 3115224471290,18654716694895,111741999352603,669466118302169
%N A124294 Number of free generators of degree n of symmetric polynomials in 6-noncommuting 
               variables.
%C A124294 Also the number of non-splitable set partitions (see Bergeron et. al. 
               reference) of length <=6
%D A124294 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 A124294 M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math. 
               J. 2 (1936), 626-637.
%F A124294 O.g.f. (1-14*q+68*q^2-135*q^3+91*q^4)/(1-15*q+81*q^2-192*q^3+189*q^4-53*q^5) 
               = (1 - 1/(sum_{k=0}^6 q^k/(prod_{i=1}^k (1-i*q))))/q a(n) = add( 
               A055105(n,k), k=1..6) = add(A055106(n,k),k=1..5)
%Y A124294 Cf. A055105, A055106, A055107, A074664, A001519, A124292, A124293, A124295.
%Y A124294 Sequence in context: A130579 A107945 A014330 this_sequence A124295 A074664 
               A091768
%Y A124294 Adjacent sequences: A124291 A124292 A124293 this_sequence A124295 A124296 
               A124297
%K A124294 nonn
%O A124294 1,3
%A A124294 Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24 2006