# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a007994 Showing 1-1 of 1 %I A007994 #25 Feb 07 2024 09:00:23 %S A007994 4,22,110,453,1482,4083,9926,21959,45122,87347,160922,284310,484528, %T A007994 800206,1285462,2014746,3088824,4642092,6851430,9946827,14224030, %U A007994 20059493,27927926,38422769,52279942,70405249,93905842,124126180 %N A007994 Poincaré series (or Poincare series) of Lie algebra associated with a certain braid group. %C A007994 The series in the Humphries paper has zeros interleaved. %D A007994 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. %H A007994 Vincenzo Librandi, Table of n, a(n) for n = 1..1000 %H A007994 S. P. Humphries, Home page. %H A007994 Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). %F A007994 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 %F A007994 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 %t A007994 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 *) %K A007994 nonn,easy %O A007994 1,1 %A A007994 _Stephen P. Humphries_ %E A007994 More terms from _Ralf Stephan_, Jun 11 2005 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE