A007994 Poincaré series (or Poincare series) of Lie algebra associated with a certain braid group.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A007991 A007992 A007993 * A007995 A007996 A007997

Keyword

nonn,easy

Author

Stephen P. Humphries

Extensions

More terms from Ralf Stephan, Jun 11 2005

Status

approved