cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A198085 #16 Feb 04 2021 14:14:52
%S A198085 1,3,11,114,6833,7783197,2414627236077,56130437209370100252470
%N 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).
%C A198085 The restriction to (spanning hypergraphs = maximal antichains = clutters on [n]) is considered in A048143.
%F A198085 a(n) = Sum_{k=1..n} binomial(n,k) * A048143(k). - _Andrew Howroyd_, Feb 04 2021
%e A198085 For n=3: {{1}}, {{2}}, {{3}}, {{12}}, {{13}}, {{23}}, {{123}}, {{12}{13}}, {{12}{23}}, {{13}{23}}, {{12}{13}{23}}.
%Y A198085 Cf. A048143.
%K A198085 nonn,more
%O A198085 1,2
%A A198085 _Gus Wiseman_, Oct 21 2011
%E A198085 a(6)-a(8) from _Andrew Howroyd_, Feb 04 2021