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%I #5 Feb 16 2022 23:21:26
%S 1,1,1,2,2,3,5,8,11,18,29,49,83,148,267,507,977,1958,4041,8626,18942
%N Let X be the poset of finite subsets of the positive integers. The sequence is the number of downsets in X of cardinality n modulo equivalence by permutations of the positive integers.
%C a(21) took about 78 hours to compute on a fast DEC alpha (using Magma).
%e a(5) = 2 because the only example up to permutation are {{},{1},{2},{1,2},{3}} {{},{1},{2},{3},{4}}.
%K hard,more,nonn,nice
%O 1,4
%A _Victor S. Miller_, Sep 30 2003
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