OFFSET
0,3
COMMENTS
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.
Also, Eulerian D-polynomials (A066094) evaluated at 2. - Ralf Stephan, Apr 23 2004
REFERENCES
Kenneth S. Brown, Buildings, Springer-Verlag, 1988
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Joël Gay, Vincent Pilaud, The weak order on Weyl posets, arXiv:1804.06572 [math.CO], 2018.
FORMULA
a(0)=a(1)=1. For n>1, a(n)=1 + sum('2^r*binomial(n, r)*a(n-r)', 'r'=1..n)
E.g.f: (2*x-exp(x))/(exp(2*x)-2) - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 14 2003
a(n) ~ n! * (sqrt(2)/log(2)-1)/2 * (2/log(2))^n. - Vaclav Kotesovec, Oct 08 2013
MATHEMATICA
CoefficientList[Series[(2*x-E^x)/(E^(2*x)-2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 08 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Boddington & Tim Honeywill, Feb 10 2003
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 14 2003
STATUS
approved