|
Search: id:A124295
|
|
|
| A124295 |
|
Number of free generators of degree n of symmetric polynomials in 7-noncommuting variables. |
|
+0
5
|
|
| 1, 1, 2, 6, 22, 92, 426, 2145, 11589, 66425, 399682, 2500037, 16115347, 106266473, 712602272, 4837372576, 33128183406, 228308233098, 1580495251012, 10976092266889, 76398165848091, 532614662149795, 3717370694711130
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Also the number of non-splitable set partitions (see Bergeron et. al. reference) of length <=7
|
|
REFERENCES
|
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
M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math. J. 2 (1936), 626-637.
|
|
FORMULA
|
O.g.f. (1-20*q+151*q^2-535*q^3+881*q^4-531*q^5)/(1-21*q+170*q^2-669*q^3+1314*q^4-1157*q^5+309*q^6) = (1 - 1/(sum_{k=0}^7 q^k/(prod_{i=1}^k (1-i*q))))/q a(n) = add( A055105(n,k), k=1..7) = add(A055106(n,k),k=1..6)
|
|
CROSSREFS
|
Cf. A055105, A055106, A055107, A074664, A001519, A124292, A124293, A124294.
Adjacent sequences: A124292 A124293 A124294 this_sequence A124296 A124297 A124298
Sequence in context: A107945 A014330 A124294 this_sequence A074664 A091768 A109317
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 24 2006
|
|
|
Search completed in 0.002 seconds
|
