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

Author

Gus Wiseman, May 23 2018

Keywords

• nonn
• more

Comments

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

Examples

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

Links

• 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.

Crossrefs

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

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

Formula

Exponential transform of A304985.

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

Extensions

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

a(9) from Aniruddha Biswas, May 12 2024