A124294 Number of free generators of degree n of symmetric polynomials in 6-noncommuting variables.

1, 1, 2, 6, 22, 92, 425, 2119, 11184, 61499, 347980, 2007643, 11734604, 69181578, 410179429, 2441025998, 14562284120, 87012222100, 520458020949, 3115224471290, 18654716694895, 111741999352603, 669466118302169

Offset

1,3

Comments

Also the number of non-splitable set partitions (see Bergeron et al. reference) of length <=6

Links

Table of n, a(n) for n=1..23.

N. Bergeron, C. Reutenauer, M. Rosas and M. Zabrocki, Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables, arXiv:math/0502082 [math.CO], 2005; Canad. J. Math. 60 (2008), no. 2, 266-296.

M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math. J. 2 (1936), 626-637.

Index entries for linear recurrences with constant coefficients, signature (15, -81, 192, -189, 53).

Formula

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)

Mathematica

LinearRecurrence[{15, -81, 192, -189, 53}, {1, 1, 2, 6, 22}, 23] (* Jean-François Alcover, Dec 04 2018 *)

Crossrefs

Cf. A055105, A055106, A055107, A074664, A001519, A124292, A124293, A124295.

Sequence in context: A279571 A014330 A225294 * A124295 A074664 A367442

Adjacent sequences: A124291 A124292 A124293 * A124295 A124296 A124297

Keyword

nonn

Author

Mike Zabrocki, Oct 24 2006

Status

approved