A367904 Number of sets of nonempty subsets of {1..n} with only one possible way to choose a sequence of different vertices of each edge.

1, 2, 6, 38, 666, 32282, 3965886, 1165884638, 792920124786, 1220537093266802, 4187268805038970806, 31649452354183112810198, 522319168680465054600480906, 18683388426164284818805590810122, 1439689660962836496648920949576152046, 237746858936806624825195458794266076911118

Offset: 0

Author

Gus Wiseman, Dec 08 2023

Keywords

• nonn

Examples

			The set-system Y = {{1},{1,2},{2,3}} has choices (1,1,2), (1,1,3), (1,2,2), (1,2,3), of which only (1,2,3) has all different elements, so Y is counted under a(3).
The a(0) = 1 through a(2) = 6 set-systems:
  {}  {}     {}
      {{1}}  {{1}}
             {{2}}
             {{1},{2}}
             {{1},{1,2}}
             {{2},{1,2}}
		

Links

• Christian Sievers, Table of n, a(n) for n = 0..77

Crossrefs

The maximal case (n subsets) is A003024.

The version for at least one choice is A367902.

The version for no choices is A367903, no singletons A367769, ranks A367907.

These set-systems have ranks A367908, nonzero A367906.

A000372 counts antichains, covering A006126, nonempty A014466.

A003465 counts covering set-systems, unlabeled A055621.

A058891 counts set-systems, unlabeled A000612.

A059201 counts covering T_0 set-systems.

A323818 counts covering connected set-systems, unlabeled A323819.

Cf. A102896, A133686, A283877, A306445, A355741, A367770, A367862, A367869, A367901, A367905.

Programs

Mathematica

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

Formula

a(n) = A367902(n) - A367772(n). - Christian Sievers, Jul 26 2024

Binomial transform of A003024. - Christian Sievers, Aug 12 2024

Extensions

a(5)-a(8) from Christian Sievers, Jul 26 2024

More terms from Christian Sievers, Aug 12 2024