A008666 Expansion of g.f.: 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9)).

1, 0, 1, 1, 1, 2, 3, 2, 4, 5, 5, 7, 9, 8, 12, 14, 14, 18, 22, 21, 28, 31, 32, 39, 45, 45, 55, 61, 63, 74, 83, 84, 99, 108, 112, 128, 141, 144, 165, 178, 185, 207, 225, 231, 259, 278, 288, 318, 342, 352, 389, 414, 429, 468, 500, 515, 562, 595, 616, 666, 707, 728, 787, 830, 858, 921

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 Molien series

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

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)
(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
(Sage)
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

Sequence in context: A178853 A344646 A120641 * A240854 A332900 A336150

Adjacent sequences: A008663 A008664 A008665 * A008667 A008668 A008669

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(51) onward added by G. C. Greubel, Sep 07 2019

Status

approved