%I A124293
%S A124293 1,1,2,6,22,91,406,1896,9093,44279,217500,1073657,5314870,26352107,
%T A124293 130778039,649352929,3225196431,16021584848,79597062632,395469296912,
%U A124293 1964908443531,9762920818182,48508934285620,241027326818991
%N A124293 Number of free generators of degree n of symmetric polynomials in 5-noncommuting 
               variables.
%C A124293 Also the number of non-splitable set partitions (see Bergeron et al. 
               reference) of length <=5
%D A124293 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 A124293 M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math. 
               J. 2 (1936), 626-637.
%F A124293 O.g.f. (1-9q+24q^2-19q^3)/(1-10q+32q^2-37q^3+11q^4) = (1 - 1/(sum_{k=0}^5 
               q^k/(prod_{i=1}^k (1-i*q))))/q a(n) = add( A055105(n,k), k=1..5) 
               = add(A055106(n,k),k=1..4)
%p A124293 a:= n-> (Matrix([[6,2,1,1]]). Matrix(4, (i,j)-> if i=j-1 then 1 elif 
               j=1 then [10, -32, 37, -11][i] else 0 fi)^(n-1))[1,4]: seq (a(n), 
               n=1..24); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 05 
               2008]
%Y A124293 Cf. A055105, A055106, A055107, A074664, A001519, A124292, A124294, A124295.
%Y A124293 Sequence in context: A089449 A150271 A150272 this_sequence A107591 A155866 
               A150273
%Y A124293 Adjacent sequences: A124290 A124291 A124292 this_sequence A124294 A124295 
               A124296
%K A124293 nonn
%O A124293 1,3
%A A124293 Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24 2006