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.
%I A370818 #9 Aug 12 2024 16:35:49
%S A370818 1,2,6,45,1352,157647,63380093,85147722812,385321270991130
%N A370818 Number of sets of nonempty subsets of {1..n} with only one possible way to choose a set of different vertices of each edge.
%F A370818 a(n) = A370638(2^n - 1).
%F A370818 Binomial transform of A368601. - _Christian Sievers_, Aug 12 2024
%e A370818 The set-system {{2},{1,2},{2,4},{1,3,4}} has unique choice (2,1,4,3) so is counted under a(4).
%t A370818 Table[Length[Select[Subsets[Subsets[Range[n]]], Length[Union[Sort/@Select[Tuples[#],UnsameQ@@#&]]]==1&]],{n,0,3}]
%Y A370818 This is the unique version of A367902, complement A367903.
%Y A370818 Choosing a sequence gives A367904, ranks A367908.
%Y A370818 The maximal case is A368601, complement A368600.
%Y A370818 This is the restriction of A370638 to A000225.
%Y A370818 Factorizations of this type are counted by A370645.
%Y A370818 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A370818 A058891 counts set-systems, A003465 covering, A323818 connected.
%Y A370818 A070939 gives length of binary expansion.
%Y A370818 A096111 gives product of binary indices.
%Y A370818 Cf. A133686, A134964, A367772, A367867, A368101, A368109, A370584.
%K A370818 nonn,more
%O A370818 0,2
%A A370818 _Gus Wiseman_, Mar 12 2024
%E A370818 a(5)-a(8) from _Christian Sievers_, Aug 12 2024