0,1

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

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

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.

Alessandro Conflitti, On Whitney numbers of the Order Ideals of Generalized Fences and Crowns

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)

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

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.

Cf. A051291, A051286.

Sequence in context: A096540 A111569 A055130 this_sequence A094424 A083677 A075803

Adjacent sequences: A051289 A051290 A051291 this_sequence A051293 A051294 A051295

nonn

Emanuele Munarini (munarini(AT)mate.polimi.it)

ArXiv URL replaced by non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2009