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.

1, 2, 6, 45, 1352, 157647, 63380093, 85147722812, 385321270991130

Offset: 0

Author

Gus Wiseman, Mar 12 2024

Keywords

• nonn
• more

Examples

			The set-system {{2},{1,2},{2,4},{1,3,4}} has unique choice (2,1,4,3) so is counted under a(4).
		

Crossrefs

This is the unique version of A367902, complement A367903.

Choosing a sequence gives A367904, ranks A367908.

The maximal case is A368601, complement A368600.

This is the restriction of A370638 to A000225.

Factorizations of this type are counted by A370645.

A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.

A058891 counts set-systems, A003465 covering, A323818 connected.

A070939 gives length of binary expansion.

A096111 gives product of binary indices.

Cf. A133686, A134964, A367772, A367867, A368101, A368109, A370584.

Programs

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n]]], Length[Union[Sort/@Select[Tuples[#],UnsameQ@@#&]]]==1&]],{n,0,3}]

Formula

a(n) = A370638(2^n - 1).

Binomial transform of A368601. - Christian Sievers, Aug 12 2024

Extensions

a(5)-a(8) from Christian Sievers, Aug 12 2024