A124617 Poincaré series [or Poincare series] P(T_{5,2}; x).

1, 4, 14, 42, 118, 304, 747, 1748, 3949, 8620, 18296, 37818, 76398, 151022, 292754, 557130, 1042364, 1919044, 3480203, 6221668, 10973326, 19106264, 32862300, 55865180, 93915547, 156203520, 257157134, 419217118, 676991229, 1083396912, 1718709997, 2703754666

Offset

0,2

Links

Table of n, a(n) for n=0..31.

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^32+2*x^31+x^30-2*x^29-x^28+8*x^27+20*x^26+24*x^25+18*x^24+12*x^23+20*x^22+44*x^21+76*x^20+94*x^19+85*x^18+

58*x^17+44*x^16+58*x^15+85*x^14+94*x^13+76*x^12+44*x^11+20*x^10+12*x^9+18*x^8+24*x^7+20*x^6+8*x^5-x^4-2*x^3+x^2+2*x+1,

g = (1-x)^2*(1-x^2)^6*(1-x^3)^8*(1-x^4)^6*(1-x^5)^4.

Crossrefs

Sequence in context: A335514 A221058 A347583 * A124618 A189052 A189426

Adjacent sequences: A124614 A124615 A124616 * A124618 A124619 A124620

Keyword

nonn

Author

N. J. A. Sloane, Dec 21 2006

Status

approved