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

Author

Stephen P. Humphries

Keywords

• nonn
• easy

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).

Programs

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 *)

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

Extensions

More terms from Ralf Stephan, Jun 11 2005