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A007993 Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group. 1
3, 12, 40, 102, 219, 419, 738, 1221, 1923, 2910, 4260, 6064, 8427, 11469, 15326, 20151, 26115, 33408, 42240, 52842, 65467, 80391, 97914, 118361, 142083, 169458, 200892, 236820, 277707, 324049, 376374, 435243, 501251, 575028, 657240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The series in the Humphries paper has zeros interleaved.

LINKS

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

S. P. Humphries, Home page

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 (6,-15,20,-15,6,-1).

FORMULA

a(n) = 3 + 9(n-1) + 19(n-1)(n-2)/2 + 15(n-1)(n-2)(n-3)/6 + 6(n-1)(n-2)(n-3)(n-4)/24 + (n-1)(n-2)(n-3)(n-4)(n-5)/120. - John W. Layman, May 12 1999

a(n-1) = (1/120)(n^5 + 10n^4 + 35n^3 - 10n^2 - 396n + 720) with n>1. - Ralf Stephan, Jun 11 2005

G.f. -x*(-3+6*x-13*x^2+18*x^3-12*x^4+3*x^5) / (x-1)^6 . - R. J. Mathar, Dec 02 2011

MATHEMATICA

CoefficientList[ Series[(3 - 6x + 13x^2 - 18x^3 + 12x^4 - 3x^5) / (1 - 6x + 15x^2 - 20x^3 + 15x^4 - 6x^5 + x^6), {x, 0, 34}], x] (* Jean-François Alcover, Dec 02 2011 *)

CROSSREFS

Sequence in context: A237036 A034956 A032093 * A293366 A080929 A052482

Adjacent sequences:  A007990 A007991 A007992 * A007994 A007995 A007996

KEYWORD

nonn,easy

AUTHOR

Stephen P. Humphries

EXTENSIONS

More terms from Ralf Stephan, Jun 11 2005

STATUS

approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)