OFFSET
0,6
COMMENTS
Molien series for 5-dimensional complex reflection group of order 2^7.3^4.5 is given by 1/((1-x^4)*(1-x^6)*(1-x^10)*(1-x^12)*(1-x^18)).
a(n) is the number of partitions of n into parts 2, 3, 5, 6, and 9. - Joerg Arndt, Sep 08 2019
REFERENCES
L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 33).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 247
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,1,-1,-2,0,1,-1,-1,1,1,-1,0,2,1,-1,0,0,-1,-1,0,1).
FORMULA
a(n) ~ 1/38880*n^4 + 1/3888*n^3. - Ralf Stephan, Apr 29 2014
a(n) = floor((n^4 + 50*n^3 + 860*n^2 + 40*(n^2+18*n+54)*(((n+2) mod 3) - ((n+1) mod 3)) + (5315 + 405*(-1)^n + 560*((n+2) mod 3))*n + 36720)/38880). - Hoang Xuan Thanh, Sep 30 2025
MAPLE
seq(coeff(series(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 07 2019
MATHEMATICA
CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^5)(1-x^6)(1-x^9)), {x, 0, 70}], x] (* Harvey P. Dale, Jul 28 2012 *)
PROG
(PARI) a(n)=polcoeff(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9)) + x*O(x^n), n)
(PARI) a(n) = (n^4+50*n^3+860*n^2 + 40*(n^2+18*n+54)*(((n+2)%3)-((n+1)%3)) + (5315+405*(-1)^n+560*((n+2)%3))*n + 36720)\38880 \\ Hoang Xuan Thanh, Sep 30 2025
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9)) )); // G. C. Greubel, Sep 07 2019
(SageMath)
def AA008666_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9))).list()
AA008666_list(70) # G. C. Greubel, Sep 07 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(51) onward added by G. C. Greubel, Sep 07 2019
STATUS
approved
