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A266770 Molien series for invariants of finite Coxeter group D_7. 10
1, 0, 1, 0, 2, 0, 3, 1, 5, 1, 7, 2, 11, 3, 15, 5, 21, 7, 28, 11, 38, 15, 49, 21, 65, 28, 82, 38, 105, 49, 131, 65, 164, 82, 201, 105, 248, 131, 300, 164, 364, 201, 436, 248, 522, 300, 618, 364, 733, 436, 860, 522, 1009, 618, 1175, 733, 1367, 860, 1579, 1009, 1824, 1175, 2093, 1367, 2400, 1579, 2738, 1824, 3120, 2093, 3539, 2400, 4011 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..72.

Index entries for Molien series

FORMULA

G.f.: 1/((1-t^7)*(1-t^2)*(1-t^4)*(1-t^6)*(1-t^8)*(1-t^10)*(1-t^12)).

CROSSREFS

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

Sequence in context: A162517 A180876 A162170 * A282892 A008798 A005290

Adjacent sequences:  A266767 A266768 A266769 * A266771 A266772 A266773

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 10 2016

STATUS

approved

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)