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 A008582 Molien series for Weyl group E_8. 2
 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 14, 17, 20, 25, 28, 34, 40, 47, 54, 64, 72, 85, 97, 111, 126, 146, 163, 187, 211, 238, 266, 302, 335, 378, 421, 469, 520, 582, 640, 712, 786, 868, 954, 1055, 1153, 1270, 1391, 1523, 1662, 1822, 1979, 2162, 2352, 2558, 2774, 3018, 3262 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES Coxeter and Moser, Generators and Relations for Discrete Groups, Table 10. L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 37). LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 252 FORMULA G.f.: 1/((1-x^2)*(1-x^8)*(1-x^12)*(1-x^14)*(1-x^18)*(1-x^20)*(1-x^24)*(1-x^30)). a(n) ~ 1/13716864000*n^7 (for the sequence without interleaved zeros). - Ralf Stephan, Apr 29 2014 MAPLE seq(coeff(series( mul(1/((1-x^(3*j+6))*(1-x^(3*j+1))), j=0..3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Feb 02 2020 MATHEMATICA Select[CoefficientList[Series[1/((1-x^2)(1-x^8)(1-x^12)(1-x^14)(1-x^18) (1-x^20)(1-x^24)(1-x^30)), {x, 0, 180}], x], #!=0&] (* Harvey P. Dale, Jun 09 2011 *) CoefficientList[Series[Product[1/((1-x^(3*j+6))*(1-x^(3*j+1))), {j, 0, 3}], {x, 0, 60}], x] (* G. C. Greubel, Feb 02 2020 *) PROG (Magma) MolienSeries(CoxeterGroup("E8")); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006 (PARI) Vec( prod(j=0, 3, 1/((1-x^(3*j+6))*(1-x^(3*j+1)))) +O('x^60) ) \\ G. C. Greubel, Feb 02 2020 (Sage) def A008582_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( product(1/((1-x^(3*j+6))*(1-x^(3*j+1))) for j in (0..3)) ).list() A008582_list(60) # G. C. Greubel, Feb 02 2020 CROSSREFS Sequence in context: A319069 A029013 A114096 * A069911 A185225 A027196 Adjacent sequences: A008579 A008580 A008581 * A008583 A008584 A008585 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified January 28 22:06 EST 2023. Contains 359905 sequences. (Running on oeis4.)