A305000 Number of labeled antichains of finite sets spanning some subset of {1,...,n} with singleton edges allowed.

1, 2, 8, 72, 1824, 220608, 498243968, 309072306743552, 14369391925598802012151296

Offset

0,2

Comments

Only the non-singleton edges are required to form an antichain.

Links

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

Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Formula

Binomial transform of A304999.

Example

The a(2) = 8 antichains:
  {}
  {{1}}
  {{2}}
  {{1,2}}
  {{1},{2}}
  {{1},{1,2}}
  {{2},{1,2}}
  {{1},{2},{1,2}}

Crossrefs

Cf. A006126, A261005, A304996, A304997, A304998, A304999, A305000, A305001.

Cf. A000372, A003182, A014466, A293606, A293993, A306505, A320449, A321679.

Sequence in context: A342177 A125814 A295044 * A013002 A012998 A143760

Adjacent sequences: A304997 A304998 A304999 * A305001 A305002 A305003

Keyword

nonn,more

Author

Gus Wiseman, May 23 2018

Extensions

a(5)-a(8) from Gus Wiseman, May 31 2018

Status

approved