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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, Gens. and Relations for Discrete Grps, 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

Index entries for Molien series

FORMULA

a(n) ~ 1/13716864000*n^7 (for the sequence without interleaved zeros). - Ralf Stephan, Apr 29 2014

MAPLE

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));

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 *)

PROG

(MAGMA) MolienSeries(CoxeterGroup("E8")); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006

CROSSREFS

Sequence in context: A319069 A029013 A114096 * A069911 A185225 A027196

Adjacent sequences:  A008579 A008580 A008581 * A008583 A008584 A008585

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 14 12:21 EST 2019. Contains 329114 sequences. (Running on oeis4.)