%I A051291
%S A051291 1,2,3,7,17,40,97,238,587,1458,3640,9124,22951,57904,146461,371281,
%T A051291 943045,2399460,6114555,15603339,39866932,101976512,261117378,
%U A051291 669239402,1716737267,4407306170,11323050897,29110603423,74888578067
%N A051291 Whitney number of level n of the lattice of the ideals of the fence of 
               order 2 n + 1.
%C A051291 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 A051291 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 A051291 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 A051291 a(2) = 3 because the ideals of size 2 of the fence F(5) = { x1 < x2 > 
               x3 < x4 > x5 } are x1x2, x1x3, x2x3.
%Y A051291 Cf. A051286, A051292.
%Y A051291 Sequence in context: A105554 A145230 A135364 this_sequence A143013 A113483 
               A059801
%Y A051291 Adjacent sequences: A051288 A051289 A051290 this_sequence A051292 A051293 
               A051294
%K A051291 nonn
%O A051291 0,2
%A A051291 Emanuele Munarini (munarini(AT)mate.polimi.it)