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%I #18 Mar 03 2024 14:28:52
%S 1,1,2,6,22,92,425,2119,11184,61499,347980,2007643,11734604,69181578,
%T 410179429,2441025998,14562284120,87012222100,520458020949,
%U 3115224471290,18654716694895,111741999352603,669466118302169
%N Number of free generators of degree n of symmetric polynomials in 6-noncommuting variables.
%C Also the number of non-splitable set partitions (see Bergeron et al. reference) of length <=6
%H N. Bergeron, C. Reutenauer, M. Rosas and M. Zabrocki, <a href="https://arxiv.org/abs/math/0502082">Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables</a>, arXiv:math/0502082 [math.CO], 2005; Canad. J. Math. 60 (2008), no. 2, 266-296.
%H M. C. Wolf, <a href="http://dx.doi.org/10.1215/S0012-7094-36-00253-3">Symmetric functions of noncommutative elements</a>, Duke Math. J. 2 (1936), 626-637.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15, -81, 192, -189, 53).
%F 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)
%t LinearRecurrence[{15, -81, 192, -189, 53}, {1, 1, 2, 6, 22}, 23] (* _Jean-François Alcover_, Dec 04 2018 *)
%Y Cf. A055105, A055106, A055107, A074664, A001519, A124292, A124293, A124295.
%K nonn
%O 1,3
%A _Mike Zabrocki_, Oct 24 2006
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