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%I #5 Mar 19 2015 09:40:24
%S 1,2,3,7,17,40,97,238,587,1458,3640,9124,22951,57904,146461,371281,
%T 943045,2399460,6114555,15603339,39866932,101976512,261117378,
%U 669239402,1716737267,4407306170,11323050897,29110603423,74888578067
%N Whitney number of level n of the lattice of the ideals of the fence of order 2 n + 1.
%C 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_, May 07 2008
%D 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.
%F G.f.: function = (1+2*t^2-t^3-(1-t)*sqrt(1-2*t-t^2-2*t^3+t^4))/(2*t*sqrt(1-2*t-t^2-2*t^3+t^4))
%e a(2) = 3 because the ideals of size 2 of the fence F(5) = { x1 < x2 > x3 < x4 > x5 } are x1x2, x1x3, x2x3.
%Y Cf. A051286, A051292.
%K nonn
%O 0,2
%A _Emanuele Munarini_