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A266771 Molien series for invariants of finite Coxeter group D_8 (bisected). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

Table of n, a(n) for n=0..49.

Index entries for Molien series

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.

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 *)

CROSSREFS

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

Sequence in context: A068491 A239952 A240076 * A295342 A226635 A024788

Adjacent sequences:  A266768 A266769 A266770 * A266772 A266773 A266774

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 10 2016

STATUS

approved

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)