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