%I #17 Mar 10 2019 15:18:28
%S 1,2,4,8,14,24,40,63,96,144,210,300,422,582,791,1062,1406,1840,2384,
%T 3056,3882,4891,6110,7576,9330,11412,13872,16766,20149,24088,28658,
%U 33932,39998,46952,54890,63925,74178,85772,98848,113558,130056,148516,169125,192072
%N G.f.: Product((1+x^i)/(1-x^i),i=1..n-1)/(1-x^n), with n = 7.
%C Poincaré series [or Poincare series] (or Molien series) for H^*(O_7(q); F_2).
%D A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 233.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-6,7,-6,7,-9,10,-9,9,-10,9,-7,6,-7,6,-3,3,-3,1).
%F G.f.: -(x^2+1)*(x^4-x^3+x^2-x+1)*(x^4-x^2+1)*(x^4+1) / ((x-1)^7*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)). [_Colin Barker_, Jan 31 2013]
%t CoefficientList[Series[(Product[(1+x^i)/(1-x^i),{i,6}])/(1-x^7),{x,0,50}],x] (* or *) LinearRecurrence[{3,-3,3,-6,7,-6,7,-9,10,-9,9,-10,9,-7,6,-7,6,-3,3,-3,1},{1,2,4,8,14,24,40,63,96,144,210,300,422,582,791,1062,1406,1840,2384,3056,3882},50] (* _Harvey P. Dale_, Mar 10 2019 *)
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Mar 18 2004