OFFSET
0,5
COMMENTS
The Molien series for the finite Coxeter group of type D_k (k >= 3) has G.f. = 1/Prod_i (1-x^(1+m_i)) where the m_i are [1,3,5,...,2k-3,k-1]. If k is even only even powers of x appear, and we bisect the sequence.
REFERENCES
J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.1, page 59.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1/((1-t^2)*(1-t^4)*(1-t^6)*(1-t^8)*(1-t^9)*(1-t^10)*(1-t^12)*(1-t^14)*(1-t^16)).
MAPLE
seq(coeff(series(1/((1-x^9)*mul(1-x^(2*j), j=1..8)), x, n+1), x, n), n = 0..80); # G. C. Greubel, Feb 03 2020
MATHEMATICA
CoefficientList[Series[1/((1-x^9)*Product[1-x^(2*j), {j, 8}]), {x, 0, 80}], x] (* G. C. Greubel, Feb 03 2020 *)
PROG
(PARI) Vec(1/((1-x^9)*prod(j=1, 8, 1-x^(2*j))) +O('x^80)) \\ G. C. Greubel, Feb 03 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^9)*(&*[1-x^(2*j): j in [1..8]])) )); // G. C. Greubel, Feb 03 2020
(Sage)
def A266772_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^9)*product(1-x^(2*j) for j in (1..8))) ).list()
A266772_list(80) # G. C. Greubel, Feb 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 11 2016
STATUS
approved