A124618 Poincaré series [or Poincare series] P(T_{6,2}; x).

1, 4, 14, 42, 118, 310, 779, 1876, 4382, 9948, 22057, 47850, 101844, 212946, 438118, 887814, 1773827, 3496850, 6806682, 13089748, 24882962, 46778368, 87005834, 160168440, 291935815, 527013208, 942571346, 1670669524, 2935415726, 5114032028, 8836476737

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Dragomir Z. Djokovic, Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices. See Table 4.

Formula

G.f.: f/g where

f = x^60-3*x^59+4*x^58-4*x^57+4*x^56+3*x^55-6*x^54+11*x^53-12*x^52+12*x^51+12*x^50+x^49+55*x^48-22*x^47+82*x^46+

77*x^44+119*x^43+84*x^42+234*x^41+160*x^40+227*x^39+312*x^38+207*x^37+507*x^36+301*x^35+612*x^34+469*x^33+

517*x^32+593*x^31+426*x^30+593*x^29+517*x^28+469*x^27+612*x^26+301*x^25+507*x^24+207*x^23+312*x^22+227*x^21+

160*x^20+234*x^19+84*x^18+119*x^17+77*x^16+82*x^14-22*x^13+55*x^12+x^11+12*x^10+12*x^9-12*x^8+11*x^7-6*x^6+3*x^5+

4*x^4-4*x^3+4*x^2-3*x+1,

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

Crossrefs

Sequence in context: A221058 A347583 A124617 * A189052 A189426 A007076

Adjacent sequences: A124615 A124616 A124617 * A124619 A124620 A124621

Keyword

nonn

Author

N. J. A. Sloane, Dec 21 2006

Status

approved