%I
%S 3,6,18,42,94,180,348,602,1047,1692,2737,4194,6426,9450,13863,19716,
%T 27933,38616,53160,71748,96396,127440,167704,217740,281439,359654,
%U 457617,576630,723592,900396,1116033,1373166,1683327,2050212,2488416,3002934,3612072
%N PoincarĂ© series [or Poincare series] of Lie algebra associated with a certain braid group.
%H Colin Barker, <a href="/A007990/b007990.txt">Table of n, a(n) for n = 2..1000</a>
%H S. P. Humphries, <a href="https://doi.org/10.1016/S01668641(98)000078">Braid groups, infinite Lie algebras of Cartan type and rings of invariants</a>, Topology and its Applications, 95 (3) (1999) pp. 173205.
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,6,5,4,10,4,12,8,0,8,12,4,10,4,5,6,3,2,1).
%F The Humphries paper gives a g.f. with denominator (1x^4)*(1x^3)^2*(1x^2)^4*(1x)^2.  _Ralf Stephan_, Jun 11 2005
%F G.f.: x^2*(3  3*x^2 + 6*x^3 + 7*x^4  8*x^5  6*x^6  4*x^7 + 13*x^8 + 8*x^9  8*x^11  14*x^12 + 6*x^13 + 6*x^14 + 6*x^15  3*x^16  6*x^17 + 3*x^18) / ((1  x)^9*(1 + x)^5*(1 + x^2)*(1 + x + x^2)^2).  _Colin Barker_, Aug 02 2017
%o (PARI) Vec(x^2*(3  3*x^2 + 6*x^3 + 7*x^4  8*x^5  6*x^6  4*x^7 + 13*x^8 + 8*x^9  8*x^11  14*x^12 + 6*x^13 + 6*x^14 + 6*x^15  3*x^16  6*x^17 + 3*x^18) / ((1  x)^9*(1 + x)^5*(1 + x^2)*(1 + x + x^2)^2) + O(x^50)) \\ _Colin Barker_, Aug 03 2017
%K nonn,easy
%O 2,1
%A _Stephen P. Humphries_
%E More terms from _Ralf Stephan_, Jun 11 2005
