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%I #18 Mar 15 2024 09:46:50
%S 1,2,6,14,34,68,144,276,534,974,1774,3106,5410,9146,15334,25158,40884,
%T 65264,103204,160808,248222,378350,571534,853890,1264962,1855638,
%U 2700490,3895626,5577846,7923072,11176164,15650712,21774473,30092868,41337096,56434524
%N Poincaré series [or Poincare series] P(C_{4,2}; 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, lines 6 and 7, also Table 5, lines 3-7.
%H <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, signature (3, 1, -6, -4, -6, 26, 24, -14, -46, -88, 46, 135, 125, -15, -304, -198, 34, 366, 404, -108, -384, -480, 0, 480, 384, 108, -404, -366, -34, 198, 304, 15, -125, -135, -46, 88, 46, 14, -24, -26, 6, 4, 6, -1, -3, 1).
%F G.f.: (1-x^2+x^4)*(1-x-x^3+x^4+2*x^5+x^6-x^7-x^9+x^10) / ((1-x)^3*(1-x^2)^4*(1-x^3)^5*(1-x^4)^5).
%t CoefficientList[Series[(1-x^2+x^4)*(1-x-x^3+x^4+2*x^5+x^6-x^7-x^9+x^10) / ((1-x)^3*(1-x^2)^4*(1-x^3)^5*(1-x^4)^5),{x,0,35}],x] (* _Stefano Spezia_, Mar 14 2024 *)
%Y Cf. A124637.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 21 2006
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