OFFSET
0,5
COMMENTS
The Molien series for the finite Coxeter group of type A_k (k >= 1) has g.f. = 1/Product_{i=2..k+1} (1 - x^i).
Note that this is the root system A_k, not the alternating group Alt_k.
REFERENCES
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
LINKS
Ray Chandler, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 2, 3, 3, 3, 2, 1, 0, -2, -3, -4, -4, -5, -3, -1, 1, 3, 4, 5, 5, 4, 3, 1, -1, -3, -5, -4, -4, -3, -2, 0, 1, 2, 3, 3, 3, 2, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 1, 1, 1, 0, -1).
FORMULA
G.f.: 1/((1-t^2)*(1-t^3)*(1-t^4)*(1-t^5)*(1-t^6)*(1-t^7)*(1-t^8)*(1-t^9)*(1-t^10)*(1-t^11)).
MAPLE
seq(coeff(series(1/mul(1-x^j, j=2..11), x, n+1), x, n), n = 0..70); # G. C. Greubel, Feb 03 2020
MATHEMATICA
CoefficientList[Series[1/Product[1-x^j, {j, 2, 11}], {x, 0, 70}], x] (* G. C. Greubel, Feb 03 2020 *)
PROG
(PARI) Vec( 1/prod(j=2, 11, 1-x^j) +O('x^70)) \\ G. C. Greubel, Feb 03 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/(&*[1-x^j: j in [2..11]]) )); // G. C. Greubel, Feb 03 2020
(Sage)
def A266779_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/product(1-x^j for j in (2..11))) ).list()
A266779_list(70) # G. C. Greubel, Feb 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 11 2016
STATUS
approved