A008584 revision #24
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A008584
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Molien series for Weyl group E_6.
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4
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,7
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REFERENCES
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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).
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LINKS
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FORMULA
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G.f. 1/((1-x^2)*(1-x^5)*(1-x^6)*(1-x^8)*(1-x^9)*(1-x^12))
a(n) ~ 1/6220800*n^5 + 1/414720*n^4. - Ralf Stephan, Apr 29 2014
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MATHEMATICA
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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] (* Harvey P. Dale, Aug 10 2011 *)
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PROG
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(MAGMA) MolienSeries(CoxeterGroup("E6")); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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proposed
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