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A007990 Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group. 1

%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 Poincaré 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/S0166-8641(98)00007-8">Braid groups, infinite Lie algebras of Cartan type and rings of invariants</a>, Topology and its Applications, 95 (3) (1999) pp. 173-205.

%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 (1-x^4)*(1-x^3)^2*(1-x^2)^4*(1-x)^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

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Last modified December 9 22:27 EST 2019. Contains 329880 sequences. (Running on oeis4.)