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A008583
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Molien series for Weyl group E_7.
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3
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1, 1, 1, 2, 3, 4, 6, 8, 10, 14, 18, 22, 29, 36, 44, 55, 67, 80, 98, 117, 138, 165, 194, 226, 266, 309, 356, 413, 475, 542, 622, 708, 802, 911, 1029, 1157, 1304, 1462, 1633, 1827, 2036, 2261, 2514, 2785
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OFFSET
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0,4
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COMMENTS
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The relevant generating function 1/((1-z^2)*(1-z^6)*(1-z^8)*(1-z^10)*(1-z^12)*(1-z^14)*(1-z^18)) is reduced with z^2=x below to indicate that the intermediate zeros are not stored in this sequence.
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REFERENCES
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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. 36).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 0, 0, 0, -1, -1, 0, -1, 0, 1, 0, 2, 0, 1, 0, 0, -1, 0, -2, 0, -1, 0, 1, 0, 1, 1, 0, 0, 0, -1, 0, -1, 1).
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FORMULA
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G.f.: 1/((1-x)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^9)).
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MAPLE
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A008583_list := proc(n) local G, j;
G:= series(1/((1-x)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^9)), x, n+1);
[seq(coeff(G, x, j), j=0..n)];
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MATHEMATICA
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CoefficientList[Series[1/((1-x)(1-x^3)(1-x^4)(1-x^5)(1-x^6)(1-x^7)(1-x^9)), {x, 0, 50}], x] (* Harvey P. Dale, Mar 04 2013 *)
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PROG
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(Magma) MolienSeries(CoxeterGroup("E7")); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
(PARI) A008583_list(n)=Vec(1/((1-x)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^9))+O(x^n)) /* returns n terms [a(0), ..., a(n-1)] */ \\ M. F. Hasler, Mar 26 2012
(Sage)
R.<t> = PowerSeriesRing(ZZ)
G = 1/((1-t)*(1-t^3)*(1-t^4)*(1-t^5)*(1-t^6)*(1-t^7)*(1-t^9) + O(t^n))
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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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approved
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