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A007994
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Poincaré series (or Poincare series) of Lie algebra associated with a certain braid group.
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1
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4, 22, 110, 453, 1482, 4083, 9926, 21959, 45122, 87347, 160922, 284310, 484528, 800206, 1285462, 2014746, 3088824, 4642092, 6851430, 9946827, 14224030, 20059493, 27927926, 38422769, 52279942, 70405249, 93905842, 124126180
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OFFSET
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1,1
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COMMENTS
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The series in the Humphries paper has zeros interleaved.
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REFERENCES
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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.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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a(n) = (1/362880)*(n^9 + 36*n^8 + 546*n^7 + 4536*n^6 + 19425*n^5 + 37044*n^4 - 592516*n^3 - 41616*n^2 + 7104384*n - 9434880). - Ralf Stephan, Jun 11 2005
G.f.: x*(8*x^9-54*x^8+144*x^7-178*x^6+60*x^5+102*x^4-137*x^3+70*x^2-18*x+4) / (x-1)^10. - Colin Barker, Nov 28 2012
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MATHEMATICA
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CoefficientList[Series[(8 x^9 - 54 x^8 + 144 x^7 - 178 x^6 + 60 x^5 + 102 x^4 - 137 x^3 + 70 x^2 - 18 x + 4)/(x - 1)^10, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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