A304999 Number of labeled antichains of finite sets spanning n vertices with singleton edges allowed.

1, 1, 5, 53, 1577, 212137, 496946349, 309068823607069, 14369391923126237496803793, 146629927766168786109802623629262590838145873

Offset

0,3

Comments

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

Links

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

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

Aniruddha Biswas and Palash Sarkar, Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See p. 4.

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

Formula

Exponential transform of A304985.

Inverse binomial transform of A305000. - Aniruddha Biswas, May 12 2024

Example

The a(2) = 5 antichains:
  {{1,2}}
  {{1},{2}}
  {{1},{1,2}}
  {{2},{1,2}}
  {{1},{2},{1,2}}

Crossrefs

Cf. A006126, A014466, A261005, A304996, A304997, A304998, A304999, A305000, A305001.

Cf. A000372, A003182, A304985, A305844, A306505, A319721, A321679, A324167.

Sequence in context: A330435 A113068 A099086 * A106045 A168568 A048551

Adjacent sequences: A304996 A304997 A304998 * A305000 A305001 A305002

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 12 2024

Status

approved