%I #7 Aug 03 2018 08:16:31
%S 1,0,1,9,315,64880
%N Number of caps (also clutter partitions) of clutters (connected antichains) spanning n vertices.
%C A kernel of a clutter is the restriction of the edge set to all edges contained within some connected vertex set. A clutter partition is a set partition of the edge set using kernels.
%H Gus Wiseman, <a href="http://www.mathematica-journal.com/2017/12/every-clutter-is-a-tree-of-blobs/">Every Clutter Is a Tree of Blobs</a>, The Mathematica Journal, Vol. 19, 2017.
%H Gus Wiseman, <a href="/A317634/a317634.png">All clutter partitions of non-isomorphic clutters on 4 vertices.</a>
%e The a(3) = 9 clutter partitions:
%e {{{1,2,3}}}
%e {{{1,3},{2,3}}}
%e {{{1,2},{2,3}}}
%e {{{1,2},{1,3}}}
%e {{{1,3}},{{2,3}}}
%e {{{1,2}},{{2,3}}}
%e {{{1,2}},{{1,3}}}
%e {{{1,2},{1,3},{2,3}}}
%e {{{1,2}},{{1,3}},{{2,3}}}
%Y Cf. A001187, A030019, A048143, A275307, A286520,, A293510, A304717, A317631, A317632, A317635.
%K nonn,more
%O 0,4
%A _Gus Wiseman_, Aug 02 2018
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