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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). 5
1, 1, 9, 75, 865, 12483, 216113, 4364979, 100757313, 2616517443, 75496735057, 2396212835283, 82968104980961, 3112139513814243, 125716310807844081, 5441108944839913587, 251195548533025953409, 12321551453507301079683 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000670, A080253.

Sequence in context: A231592 A126965 A066222 * A190916 A161736 A226180

Adjacent sequences:  A080251 A080252 A080253 * A080255 A080256 A080257

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

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Last modified October 15 00:04 EDT 2019. Contains 328025 sequences. (Running on oeis4.)