A266771 Molien series for invariants of finite Coxeter group D_8 (bisected).

1, 1, 2, 3, 6, 8, 13, 18, 27, 36, 51, 67, 92, 118, 156, 198, 256, 319, 404, 498, 620, 755, 926, 1116, 1353, 1615, 1935, 2291, 2720, 3194, 3759, 4384, 5120, 5932, 6879, 7923, 9131, 10458, 11981, 13654, 15561, 17648, 20014, 22600, 25514, 28692, 32255, 36134, 40464, 45167

Offset: 0

Author

N. J. A. Sloane, Jan 10 2016

Keywords

• nonn

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

• Index entries for Molien series

Crossrefs

Molien series for finite Coxeter groups D_3 through D_12 are A266755, A266769, A266768, A003402, and A266770-A266775.

Programs

Mathematica

Take[CoefficientList[Series[1/((1-x^8)Times@@(1-x^Range[2,14,2])),{x,0,100}],x],{1,-1,2}] (* Harvey P. Dale, Jan 02 2018 *)

Formula

G.f.: 1/((1-t^8)^2*(1-t^2)*(1-t^4)*(1-t^6)*(1-t^10)*(1-t^12)*(1-t^14)), bisected.