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, 146629927766168786239127150948525247729660416

Offset

0,2

Comments

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

Number of non-degenerate unate Boolean functions of n or fewer variables. - Aniruddha Biswas, May 11 2024

Links

Table of n, a(n) for n=0..9.

A. Biswas and P. Sarkar, Counting unate and balanced monotone Boolean functions, arXiv:2304.14069 [math.CO], 2023.

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

Formula

Binomial transform of A304999.

Inverse binomial transform of A245079. - Aniruddha Biswas, May 11 2024

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.

Cf. A245079.

Sequence in context: A125814 A295044 A374872 * 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

a(9) from Aniruddha Biswas, May 11 2024

Status

approved