Search: id:A124292
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%I A124292
%S A124292 1,1,2,6,21,78,297,1143,4419,17118,66366,257391,998406,3873015,15024609,
%T A124292 58285737,226111986,877174110,3402893997,13201132950,51212274057,
%U A124292 198672129783,770725711035,2989941920334,11599136512038,44997518922327
%N A124292 Number of free generators of degree n of symmetric polynomials in 4-noncommuting 
               variables.
%C A124292 Also the number of non-splitable set partitions (see Bergeron et al. 
               reference) of length <=4
%D A124292 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 A124292 M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math. 
               J. 2 (1936), 626-637.
%F A124292 O.g.f. (1-5q+5q^2)/(1-6q+9q^2-3q^3) = 1 - 1/(sum_{k=0}^4 q^k/(prod_{i=1}^k 
               (1-i*q))) a(n) = A055105(n,1)+A055105(n,2)+A055105(n,3)+A055105(n,
               4) = A055106(n,1)+A055106(n,2)+A055106(n,3)
%p A124292 a:= n-> (Matrix([[2,1,1]]). Matrix(3, (i,j)-> if i=j-1 then 1 elif j=1 
               then [6,-9,3][i] else 0 fi)^(n-1))[1,3]: seq (a(n), n=1..26); [From 
               Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 05 2008]
%Y A124292 Cf. A055105, A055106, A055107, A074664, A001519, A124293, A124294, A124295.
%Y A124292 Sequence in context: A150188 A150189 A144169 this_sequence A129776 A129775 
               A054515
%Y A124292 Adjacent sequences: A124289 A124290 A124291 this_sequence A124293 A124294 
               A124295
%K A124292 nonn
%O A124292 1,3
%A A124292 Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24 2006

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