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%I #18 Jan 30 2018 18:57:36
%S 1,0,1,1,2,2,5,4,8,9,13,15,23,24,35,40,52,60,79,87,112,127,155,177,
%T 216,240,290,326,382,430,503,557,648,720,822,914,1041,1144,1298,1428,
%U 1600,1760,1967,2146,2392,2609,2882,3142,3463,3752,4127,4468,4882,5282,5760,6202
%N G.f.: (1+x^5+x^7+x^8+x^10+x^15)/((1-x^2)(1-x^3)(1-x^4)(1-x^6)^2(1-x^9)).
%C Poincaré series [or Poincare series] (or Molien series) for (P[x_0, x_1] ⊗ P[x_0, x_1] ⊗ P[x_0, x_1] )^(S_3).
%D A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 200.
%H Ray Chandler, <a href="/A089599/b089599.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, -2, 1, -1, 0, 2, -2, 1, 0, 0, 1, -2, 2, 0, -1, 1, -2, 0, 0, 1, 1, -1).
%F G.f.: (1-x+x^5-x^9+x^10)/((1-x)^2*(1-x^2)*(1-x^4)*(1-x^6)*(1-x^9)*(1+x+x^2)). See also the NAME. - _Wolfdieter Lang_, Mar 19 2014
%o (PARI) Vec((1+x^5+x^7+x^8+x^10+x^15)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)^2*(1-x^9)) + O(x^100)) \\ _Michel Marcus_, Mar 19 2014
%Y Cf. A082146, A091434, A091726, A091769.
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Dec 31 2003
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