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A198085 Number of nonempty connected, containment-free subsets of 2^[n]. Total number of clutters on all subsets of [n]. Number of connected antichains in the Boolean algebra B_n (the poset of subsets of [n] ordered by containment). 8

%I

%S 1,3,11,114,6833,7783197,2414627236077,56130437209370100252470

%N Number of nonempty connected, containment-free subsets of 2^[n]. Total number of clutters on all subsets of [n]. Number of connected antichains in the Boolean algebra B_n (the poset of subsets of [n] ordered by containment).

%C The restriction to (spanning hypergraphs = maximal antichains = clutters on [n]) is considered in A048143.

%F a(n) = Sum_{k=1..n} binomial(n,k) * A048143(k). - _Andrew Howroyd_, Feb 04 2021

%e For n=3: {{1}}, {{2}}, {{3}}, {{12}}, {{13}}, {{23}}, {{123}}, {{12}{13}}, {{12}{23}}, {{13}{23}}, {{12}{13}{23}}.

%Y Cf. A048143.

%K nonn,more

%O 1,2

%A _Gus Wiseman_, Oct 21 2011

%E a(6)-a(8) from _Andrew Howroyd_, Feb 04 2021

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Last modified October 26 18:30 EDT 2021. Contains 348268 sequences. (Running on oeis4.)