cp's OEIS Frontend

A080254 For n>3, a(n) is the number of elements in the Coxeter complex of type D_n (although the sequence starts at n=0. See comments below for precise explanation).

%I A080254 #18 Jul 12 2018 15:51:07
%S A080254 1,1,9,75,865,12483,216113,4364979,100757313,2616517443,75496735057,
%T A080254 2396212835283,82968104980961,3112139513814243,125716310807844081,
%U A080254 5441108944839913587,251195548533025953409,12321551453507301079683
%N A080254 For n>3, a(n) is the number of elements in the Coxeter complex of type D_n (although the sequence starts at n=0. See comments below for precise explanation).
%C A080254 The sequence makes most sense when n>3. The values for a(2) and a(3) make sense if we regard D_2=A_1 x A_1 and D_3=A_3. The values for a(0) and a(1) have to be regarded as conventions and were included to give a nice recursive description. The corresponding sequence for type B is A080253. There one can find a worked example as well as a geometric interpretation.
%C A080254 Also, Eulerian D-polynomials (A066094) evaluated at 2. - _Ralf Stephan_, Apr 23 2004
%D A080254 Kenneth S. Brown, Buildings, Springer-Verlag, 1988
%H A080254 Vincenzo Librandi, <a href="/A080254/b080254.txt">Table of n, a(n) for n = 0..200</a>
%H A080254 Joël Gay, Vincent Pilaud, <a href="https://arxiv.org/abs/1804.06572">The weak order on Weyl posets</a>, arXiv:1804.06572 [math.CO], 2018.
%F A080254 a(0)=a(1)=1. For n>1, a(n)=1 + sum('2^r*binomial(n, r)*a(n-r)', 'r'=1..n)
%F A080254 E.g.f: (2*x-exp(x))/(exp(2*x)-2) - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 14 2003
%F A080254 a(n) ~ n! * (sqrt(2)/log(2)-1)/2 * (2/log(2))^n. - _Vaclav Kotesovec_, Oct 08 2013
%t A080254 CoefficientList[Series[(2*x-E^x)/(E^(2*x)-2), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 08 2013 *)
%Y A080254 Cf. A000670, A080253.
%K A080254 easy,nonn
%O A080254 0,3
%A A080254 _Paul Boddington_ & _Tim Honeywill_, Feb 10 2003
%E A080254 More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 14 2003