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

Author

Gus Wiseman, May 23 2018

Keywords

• nonn
• more

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

Examples

			The a(2) = 8 antichains:
  {}
  {{1}}
  {{2}}
  {{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 pp. 4, 12.
• Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Crossrefs

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

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

Cf. A245079.

Formula

Binomial transform of A304999.

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

Extensions

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

a(9) from Aniruddha Biswas, May 11 2024