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Poincaré series [or Poincare series] P(C_{6,2}; x).
0

%I #6 Jan 30 2018 18:57:38

%S 1,2,6,14,34,74,166,342,716,1442,2898,5686,11122,21366,40842,77098,

%T 144581,268376,494812,904056,1640304,2951812,5274356,9351868,16465309,

%U 28776074,49943314,86067486,147313950,250422502,422885538,709413626,1182445150,1958355754

%N Poincaré series [or Poincare series] P(C_{6,2}; 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 3.

%F G.f.: f/g where

%F f = x^70-3*x^69+3*x^68-3*x^67+3*x^66+4*x^65-2*x^64-8*x^62-8*x^61+11*x^60+x^59+56*x^58-24*x^57+48*x^56-69*x^55-

%F 9*x^54+2*x^53+78*x^52+118*x^51+223*x^50+23*x^49+158*x^48-182*x^47+221*x^46-42*x^45+600*x^44+365*x^43+633*x^42+

%F 324*x^41+303*x^40-31*x^39+484*x^38+178*x^37+1055*x^36+518*x^35+1055*x^34+178*x^33+484*x^32-31*x^31+303*x^30+

%F 324*x^29+633*x^28+365*x^27+600*x^26-42*x^25+221*x^24-182*x^23+158*x^22+23*x^21+223*x^20+118*x^19+78*x^18+2*x^17-

%F 9*x^16-69*x^15+48*x^14-24*x^13+56*x^12+x^11+11*x^10-8*x^9-8*x^8-2*x^6+4*x^5+3*x^4-3*x^3+3*x^2-3*x+1,

%F g = (1-x)^5*(1-x^2)^3*(1-x^3)^6*(1-x^4)^9*(1-x^5)^7*(1-x^6)^7.

%K nonn

%O 0,2

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