%I #6 Jan 30 2018 18:57:38
%S 1,4,14,42,118,304,747,1748,3949,8620,18296,37818,76398,151022,292754,
%T 557130,1042364,1919044,3480203,6221668,10973326,19106264,32862300,
%U 55865180,93915547,156203520,257157134,419217118,676991229,1083396912,1718709997,2703754666
%N Poincaré series [or Poincare series] P(T_{5,2}; x).
%H Dragomir Z. Djokovic, <a href="http://arXiv.org/abs/math.AC/0609262">Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices</a>. See Table 4.
%F G.f.: f/g where
%F f = x^32+2*x^31+x^30-2*x^29-x^28+8*x^27+20*x^26+24*x^25+18*x^24+12*x^23+20*x^22+44*x^21+76*x^20+94*x^19+85*x^18+
%F 58*x^17+44*x^16+58*x^15+85*x^14+94*x^13+76*x^12+44*x^11+20*x^10+12*x^9+18*x^8+24*x^7+20*x^6+8*x^5-x^4-2*x^3+x^2+2*x+1,
%F g = (1-x)^2*(1-x^2)^6*(1-x^3)^8*(1-x^4)^6*(1-x^5)^4.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Dec 21 2006