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A007993
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Poincare series of Lie algebra associated with a certain braid group.
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0
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| The series in the Humphries paper has zeros interleaved.
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LINKS
| 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 to sequences with linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
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FORMULA
| The polynomial 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 fits the 15 listed terms - John W. Layman (layman(AT)math.vt.edu (May 12, 1999))
(1/120) [n^5 + 10n^4 + 35n^3 - 10n^2 - 396n + 720 ]. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 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
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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] (* From Jean-François Alcover, Dec 02 2011 *)
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CROSSREFS
| Sequence in context: A062311 A034956 A032093 * A052482 A080929 A061136
Adjacent sequences: A007990 A007991 A007992 * A007994 A007995 A007996
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KEYWORD
| nonn
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AUTHOR
| Stephen P Humphries (steve(AT)math.byu.edu)
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EXTENSIONS
| More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 11 2005
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