A124635 Poincaré series [or Poincare series] P(C^o_{5,2}; x).

1, 2, 10, 37, 143, 478, 1588, 4910, 14748, 42235, 116910, 311478, 803343, 2004434, 4853669, 11414943, 26127222, 58267164, 126811068, 269647980, 560935635, 1142812869, 2282784640, 4475122564, 8618047164, 16317369805, 30400944921, 55776101043, 100842883244

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Dragomir Z. Djokovic, Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices. See Table 8.

Formula

G.f. =

(x^88+x^87+5*x^86+20*x^85+76*x^84+227*x^83+692*x^82+1933*x^81+5307*x^80+13752*x^79+34304*x^78+81525*x^77+

186346*x^76+408071*x^75+860437*x^74+1746504*x^73+3421732*x^72+6474866*x^71+11857662*x^70+21033945*x^69+

36195856*x^68+60479854*x^67+98242554*x^66+155273212*x^65+239019423*x^64+358621723*x^63+524884888*x^62+

749897456*x^61+1046516425*x^60+1427383948*x^59+1903851664*x^58+2484438301*x^57+3173436196*x^56+3969248353*x^55+

4863282209*x^54+5838905156*x^53+6871421892*x^52+7928353846*x^51+8971036674*x^50+9956478001*x^49+

10840418189*x^48+11580232480*x^47+12138549745*x^46+12485984964*x^45+12603960344*x^44+12485984964*x^43+

12138549745*x^42+11580232480*x^41+10840418189*x^40+9956478001*x^39+8971036674*x^38+7928353846*x^37+6871421892*x^36+

5838905156*x^35+4863282209*x^34+3969248353*x^33+3173436196*x^32+2484438301*x^31+1903851664*x^30+

1427383948*x^29+1046516425*x^28+749897456*x^27+524884888*x^26+358621723*x^25+239019423*x^24+155273212*x^23+

98242554*x^22+60479854*x^21+36195856*x^20+21033945*x^19+11857662*x^18+6474866*x^17+3421732*x^16+1746504*x^15+

860437*x^14+408071*x^13+186346*x^12+81525*x^11+34304*x^10+13752*x^9+5307*x^8+1933*x^7+692*x^6+227*x^5+76*x^4+

20*x^3+5*x^2+x+1) /

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

Crossrefs

Sequence in context: A034547 A246604 A124646 * A005968 A212881 A177173

Adjacent sequences: A124632 A124633 A124634 * A124636 A124637 A124638

Keyword

nonn

Author

N. J. A. Sloane, Dec 21 2006

Status

approved