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

0,2

Links

Table of n, a(n) for n=0..8.

Formula

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

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

Example

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

Mathematica

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

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.

Sequence in context: A347984 A229836 A359659 * A367916 A136557 A092662

Adjacent sequences: A370815 A370816 A370817 * A370819 A370820 A370821

Keyword

nonn,more

Author

Gus Wiseman, Mar 12 2024

Extensions

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

Status

approved