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A007994
Poincaré series (or Poincare series) of Lie algebra associated with a certain braid group.
1
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
OFFSET
1,1
COMMENTS
The series in the Humphries paper has zeros interleaved.
REFERENCES
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.
LINKS
S. P. Humphries, Home page.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
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
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A024420 A220457 A108840 * A006651 A159616 A244423
KEYWORD
nonn,easy
EXTENSIONS
More terms from Ralf Stephan, Jun 11 2005
STATUS
approved