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A124294 Number of free generators of degree n of symmetric polynomials in 6-noncommuting variables. 4
1, 1, 2, 6, 22, 92, 425, 2119, 11184, 61499, 347980, 2007643, 11734604, 69181578, 410179429, 2441025998, 14562284120, 87012222100, 520458020949, 3115224471290, 18654716694895, 111741999352603, 669466118302169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

REFERENCES

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

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.CO/0502082 , Canad. J. Math. 60 (2008), no. 2, 266-296.

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)

CROSSREFS

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

Sequence in context: A279571 A014330 A225294 * A124295 A074664 A091768

Adjacent sequences:  A124291 A124292 A124293 * A124295 A124296 A124297

KEYWORD

nonn

AUTHOR

Mike Zabrocki, Oct 24 2006

STATUS

approved

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Last modified December 12 01:08 EST 2017. Contains 295936 sequences.