%I A051292
%S A051292 2,1,1,4,9,21,52,127,313,778,1941,4863,12228,30837,77967,197574,501657,
%T A051292 1275987,3250618,8292703,21182509,54169966,138674031,355343469,
%U A051292 911347684,2339226871,6008781637,15445521202,39728258103,102248793573
%N A051292 Whitney number of level n of the lattice of the ideals of the crown of 
               size 2 n.
%C A051292 A Chebyshev transform of the central binomial numbers A002426 under the 
               mapping that takes g(x) to ((1-x^2)/(1+x^2))g(x/(1+x^2)). Starts 
               1,1,1,4,9,21,... - Paul Barry (pbarry(AT)wit.ie), Jan 31 2005
%C A051292 This is the second kind of Whitney numbers, which count elements, not 
               to be confused with the first kind, which sum Mobius functions. - 
               Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), May 07 2008
%D A051292 E. Munarini, N. Zagaglia Salvi, On the Rank Polynomial of the Lattice 
               of Order Ideals of Fences and Crowns, Discrete Mathematics 259 (2002), 
               163-177.
%H A051292 Alessandro Conflitti, <a href="http://arXiv.org/abs/math/0505636">On 
               Whitney numbers of the Order Ideals of Generalized Fences and Crowns</
               a>
%F A051292 G.f.: (1-t^2+sqrt(1-2*t-t^2-2*t^3+t^4))/sqrt(1-2*t-t^2-2*t^3+t^4)
%F A051292 a(n)=sum{k=0..floor(n/2), (n/(n-k))C(n-k, k)*(-1)^k*sum{i=0..floor((n-2k)/
               2), C(n-2k, 2i)C(2i, i)}}; a(n)=sum{k=0..floor(n/2), (n/(n-k))C(n-k, 
               k)*(-1)^k*A002426(n-2k)}. - Paul Barry (pbarry(AT)wit.ie), Jan 31 
               2005
%e A051292 a(3) = 4 because the ideals of size 3 of the crown C(3) = { x1 < x2 > 
               x3 < x4 > x5 < x6 > x1 } are x1x2x3, x3x4x5, x1x6x5, x1x3x5.
%Y A051292 Cf. A051291, A051286.
%Y A051292 Sequence in context: A096540 A111569 A055130 this_sequence A094424 A083677 
               A075803
%Y A051292 Adjacent sequences: A051289 A051290 A051291 this_sequence A051293 A051294 
               A051295
%K A051292 nonn
%O A051292 0,1
%A A051292 Emanuele Munarini (munarini(AT)mate.polimi.it)
%E A051292 ArXiv URL replaced by non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 23 2009