A124632 - OEIS

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

%S 1,0,3,4,24,44,171,388,1166,2808,7344,17281,41569,93936,211251,456531,

%T 972231,2009719,4083805,8100885,15793128,30169374,56685408,104633216,

%U 190186136,340286657,600267525,1044006248,1792246370,3037619066,5087101373,8420649189

%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 Table 7.

%F G.f. =

%F (1+x+12376177*x^63+x^85+x^83+41*x^81+329*x^79+1980*x^77+10386*x^75+47093*x^73+184182*x^71+1111589*x^68+

%F 1902191*x^67+3165521*x^66+5120359*x^65+8066607*x^64+18520117*x^62+27035364*x^61+38541637*x^60+53673328*x^59+

%F 73078953*x^58+97307914*x^57+126802726*x^56+161749890*x^55+247338162*x^53+296695937*x^52+348874713*x^51+

%F 402270954*x^50+454898759*x^49+504632564*x^48+549206297*x^47+586521387*x^46+614654835*x^45+94970*x^72+22654*x^74+

%F 4677*x^76+842*x^78+135*x^80+14*x^82+x^84+x^2+x^3+14*x^4+41*x^5+135*x^6+842*x^8+1980*x^9+4677*x^10+10386*x^11+

%F 22654*x^12+47093*x^13+94970*x^14+184182*x^15+346523*x^16+629769*x^17+1111589*x^18+1902191*x^19+3165521*x^20+

%F 5120359*x^21+8066607*x^22+12376177*x^23+18520117*x^24+27035364*x^25+346523*x^70+348874713*x^35+38541637*x^26+

%F 53673328*x^27+73078953*x^28+97307914*x^29+126802726*x^30+161749890*x^31+202084191*x^32+247338162*x^33+

%F 296695937*x^34+632178319*x^44+638112785*x^43+632178319*x^42+614654835*x^41+586521387*x^40+549206297*x^39+

%F 504632564*x^38+454898759*x^37+402270954*x^36+202084191*x^54+329*x^7+629769*x^69+x^86)/((1+x+x^2)*(1-x^2)^3*

%F (1-x^3)^3*(1-x^4)^5*(1-x^5)^5*(1-x^6)^3*(1-x^7)^2*(1-x^8)*(1-x^9)).

%K nonn

%O 0,3

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