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%I #20 May 10 2020 14:59:12
%S 5,35,235,1380,6711,26630,89695,266305,716460,1780978,4147915,9144485,
%T 19231895,38819255,75566971,142424625,260749275,464984685,809559075,
%U 1378889190,2301674475,3771041860,6072576655,9622868805,15021940010
%N Poincaré series [or Poincare series] of Lie algebra associated with a certain braid group.
%C The series in the Humphries paper has zeros interleaved.
%H S. P. Humphries, <a href="http://www.math.byu.edu/~steve/">Home page</a>
%H S. P. Humphries, <a href="http://dx.doi.org/10.1016/S0166-8641(98)00007-8">Braid groups, infinite Lie algebras of Cartan type and rings of invariants</a>, Topology and its Applications, 95 (3) (1999) pp. 173-205.
%F a(n) = (1/87178291200) [n^14 + 91*n^13 + 3731*n^12 + 91091*n^11 + 1474473*n^10 + 16429413*n^9 + 126387833*n^8 + 659772113*n^7 + 430175746*n^6 - 19046231204*n^5 - 113904491064*n^4 + 733785439296*n^3 + 1856912273280*n^2 - 12048593356800*n + 13512635136000 ]. - _Ralf Stephan_, Jun 11 2005
%F G.f.: (-45*x^15 +520*x^14 -2705*x^13 +8340*x^12 -16875*x^11 +23430*x^10 -22710*x^9 +15480*x^8 -7695*x^7 +3300*x^6 -1586*x^5 +745*x^4 -235*x^3 +40*x^2 -5*x)/(x-1)^15. - _Mark van Hoeij_, Oct 21 2011
%K nonn
%O 1,1
%A _Stephen P. Humphries_
%E More terms from _Ralf Stephan_, Jun 11 2005
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