OFFSET
0,2
REFERENCES
C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 77 (1955), 778-782.
M. C. Wolf, Symmetric functions of noncommutative elements, Duke Math. J. 2 (1936), 626-637.
LINKS
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
G.f. (1-6*q+11*q^2-6*q^3)/(1-10*q+32*q^2-37*q^3+11*q^4) more generally, sum( n!/(n-d)!*q^d/prod((1-r*q),r=1..d), d=0..n)/sum( q^d/prod((1-r*q),r=1..d), d=0..n) where n=5.
EXAMPLE
a(1) = 4 because x1-x2, x2-x3, x3-x4, x4-x5 are all of degree 1 and are killed by the differential operator d_x1+d_x2+d_x3+d_x4+d_x5.
MAPLE
coeffs(convert(series((1-6*q+11*q^2-6*q^3)/(1-10*q+32*q^2-37*q^3+11*q^4), q, 30), `+`)-O(q^30), q);
MATHEMATICA
gf = With[{n = 5}, Sum[n!/(n-d)! q^d/Product[(1 - r q), {r, 1, d}], {d, 0, n}]/Sum[ q^d/Product[(1 - r q), {r, 1, d}], {d, 0, n}]]; CoefficientList[gf + O[q]^22, q] (* Jean-François Alcover, Nov 17 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mike Zabrocki, Aug 30 2006
STATUS
approved