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%I #27 Sep 08 2022 08:44:36
%S 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,
%T 61,63,74,83,84,99,108,112,128,141,144,165,178,185,207,225,231,259,
%U 278,288,318,342,352,389,414,429,468,500,515,562,595,616,666,707,728,787,830,858,921
%N Expansion of g.f.: 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9)).
%C 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)).
%C a(n) is the number of partitions of n into parts 2, 3, 5, 6, and 9. - _Joerg Arndt_, Sep 08 2019
%D L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 33).
%H G. C. Greubel, <a href="/A008666/b008666.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=247">Encyclopedia of Combinatorial Structures 247</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, 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).
%F a(n) ~ 1/38880*n^4 + 1/3888*n^3. - _Ralf Stephan_, Apr 29 2014
%p 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
%t 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 *)
%o (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)
%o (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
%o (Sage)
%o def AA008666_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P(1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)*(1-x^9))).list()
%o AA008666_list(70) # _G. C. Greubel_, Sep 07 2019
%K nonn
%O 0,6
%A _N. J. A. Sloane_
%E Terms a(51) onward added by _G. C. Greubel_, Sep 07 2019
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