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%I #12 Mar 19 2018 04:15:13
%S 1,1,2,4,17,379,526913
%N Number of maximal antichains in the poset of Dyck paths ordered by inclusion.
%C Maximal antichains are those which cannot be extended without violating the antichain condition.
%C This is the breakdown by size of (or number of elements in) the antichains beginning with antichains of size 0 and increasing:
%C n=0: 0, 1;
%C n=1: 0, 1;
%C n=2: 0, 2;
%C n=3: 0, 3, 1;
%C n=4: 0, 3, 8, 6;
%C n=5: 0, 3, 14, 62, 132, 124, 42, 2;
%C n=6: 0, 3, 21, 157, 983, 4438, 15454, 41827, 79454, 112344, 117259, 88915, 47295, 14909, 3498, 334, 21, 1
%D R. P. Stanley, Enumerative Combinatorics 1, Cambridge University Press, New York, 1997.
%H J. Woodcock, <a href="http://garsia.math.yorku.ca/~zabrocki/dyckpathposet.html">Properties of the poset of Dyck paths ordered by inclusion</a>
%e For n = 3 there are 4 maximal antichains. Assume that the five elements in the D_3 poset are depicted using a Hasse diagram and labeled A through E from bottom to top. Then the 4 maximal antichains are {A}, {B,C}, {D}, {E}.
%Y Cf. A143672. Total number of antichains A143673.
%K nonn,more
%O 0,3
%A Jennifer Woodcock (jennifer.woodcock(AT)ugdsb.on.ca), Aug 28 2008
%E a(6) from _Alois P. Heinz_, Jul 31 2011
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