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 A007990 Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group. 1
 3, 6, 18, 42, 94, 180, 348, 602, 1047, 1692, 2737, 4194, 6426, 9450, 13863, 19716, 27933, 38616, 53160, 71748, 96396, 127440, 167704, 217740, 281439, 359654, 457617, 576630, 723592, 900396, 1116033, 1373166, 1683327, 2050212, 2488416, 3002934, 3612072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS Colin Barker, Table of n, a(n) for n = 2..1000 S. P. Humphries, Braid groups, infinite Lie algebras of Cartan type and rings of invariants, Topology and its Applications, 95 (3) (1999) pp. 173-205. Index entries for linear recurrences with constant coefficients, signature (2,3,-6,-5,4,10,4,-12,-8,0,8,12,-4,-10,-4,5,6,-3,-2,1). FORMULA 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 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 PROG (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 CROSSREFS Sequence in context: A181037 A222856 A342583 * A197050 A354387 A121188 Adjacent sequences: A007987 A007988 A007989 * A007991 A007992 A007993 KEYWORD nonn,easy AUTHOR Stephen P. Humphries EXTENSIONS More terms from Ralf Stephan, Jun 11 2005 STATUS approved

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Last modified May 29 13:20 EDT 2023. Contains 363042 sequences. (Running on oeis4.)