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Poincaré series [or Poincare series] P(C_{5,2}; x).
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%I #6 Jan 30 2018 18:57:38

%S 1,2,6,14,34,74,159,324,657,1286,2488,4702,8790,16146,29326,52526,

%T 93064,162910,282267,483792,821182,1380052,2297972,3791220,6200379,

%U 10053018,16165158,25782702,40801449,64075416,99882597,154577022,237551012,362577214,549750200

%N Poincaré series [or Poincare series] P(C_{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 Tables 3 and 5.

%F G.f.: f/g where

%F f = x^40+2*x^39-6*x^37-9*x^36+2*x^35+25*x^34+38*x^33+17*x^32-34*x^31-68*x^30-34*x^29+73*x^28+176*x^27+171*x^26+

%F 34*x^25-127*x^24-156*x^23-2*x^22+218*x^21+322*x^20+218*x^19-2*x^18-156*x^17-127*x^16+34*x^15+171*x^14+176*x^13+

%F 73*x^12-34*x^11-68*x^10-34*x^9+17*x^8+38*x^7+25*x^6+2*x^5-9*x^4-6*x^3+2*x+1,

%F g = (1-x^2)^6*(1-x^3)^8*(1-x^4)^6*(1-x^5)^6.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 21 2006