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.<x> = 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
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved