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%I #12 Jan 30 2018 18:57:39
%S 1,0,6,8,24,48,106,192,369,624,1080,1728,2787,4248,6498,9528,13962,
%T 19824,28066,38760,53334,71936,96618,127680,167983,218040,281784,
%U 360024,458037,577080,724098,900936,1116636,1373808,1684038
%N Sequence gives the Poincaré series [or Poincare series] of an ordinal Hodge algebra, or algebra with straightening law, for a ring that the braid group on four strands acts on. It is Cohen-Macaulay.
%D Stephen P. Humphries, Action of some braid groups on Hodge algebras. Comm. Algebra 26 (1998), no. 4, pages 1233-1242. See Proposition 3.4
%H Stephen P. Humphries, <a href="http://dx.doi.org/10.1080/00927879808826195">Action of some braid groups on Hodge algebras</a> Comm. Algebra 26 (1998), no. 4, pages 1233-1242. See Proposition 3.4 on page 1241.
%F G.f.: 1-(-4*x^20+8*x^19+6*x^18-12*x^17-11*x^16-2*x^15+25*x^14+10*x^13 -12*x^12) / ((1+x+x^2)^2*(1+x)^5*(1+x^2)*(1-x)^9) -(-14*x^11-15*x^10 +14*x^9+17*x^8+4*x^7-16*x^6-12*x^5+10*x^4+4*x^3-6*x^2) / ((1+x+x^2)^2*(1+x)^5*(1+x^2)*(1-x)^9).
%e For n=2 the dimension of the degree two part is 6.
%Y A053090 is a similar Poincaré series [or Poincare series] for a ring on which the three strand braid groups acts.
%K nonn,easy
%O 0,3
%A _Stephen P. Humphries_, Feb 06 2009
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