The On-Line Encyclopedia of Integer Sequences (OEIS)

A008584 revision #15

A008584

Molien series for Weyl group E_6.

1, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 6, 4, 8, 6, 10, 9, 14, 11, 18, 15, 22, 20, 29, 25, 36, 32, 43, 41, 54, 49, 66, 61, 78, 75, 95, 89, 113, 107, 132, 129, 157, 150, 184, 178, 212, 209, 248, 241, 287, 280, 327

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OFFSET

0,7

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 125.

H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups. Ergebnisse der Mathematik und Ihrer Grenzgebiete, New Series, no.14. Springer Verlag, 1957, Table 10.

L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 35).

LINKS

T. D. Noe, Table of n, a(n) for n=0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 248

Index entries for Molien series

FORMULA

G.f. 1/((1-x^2)*(1-x^5)*(1-x^6)*(1-x^8)*(1-x^9)*(1-x^12))

MATHEMATICA

CoefficientList[Series[1/((1-x^2)(1-x^5)(1-x^6)(1-x^8)(1-x^9)(1-x^12)), {x, 0, 55}], x] (* From Harvey P. Dale, Aug 10 2011 *)

PROG

(MAGMA) MolienSeries(CoxeterGroup("E6")); - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

CROSSREFS