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A008666 Expansion of g.f.: 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9)). 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(51) onward added by G. C. Greubel, Sep 07 2019
STATUS
approved

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Last modified March 19 03:30 EDT 2024. Contains 370952 sequences. (Running on oeis4.)