cp's OEIS Frontend

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

%I A305000 #35 May 02 2025 01:27:35
%S A305000 1,2,8,72,1824,220608,498243968,309072306743552,
%T A305000 14369391925598802012151296,
%U A305000 146629927766168786239127150948525247729660416
%N A305000 Number of labeled antichains of finite sets spanning some subset of {1,...,n} with singleton edges allowed.
%C A305000 Only the non-singleton edges are required to form an antichain.
%C A305000 Number of non-degenerate unate Boolean functions of n or fewer variables. - _Aniruddha Biswas_, May 11 2024
%H A305000 Aniruddha Biswas and Palash Sarkar, <a href="https://arxiv.org/abs/2304.14069">Counting unate and balanced monotone Boolean functions,</a> arXiv:2304.14069 [math.CO], 2023.
%H A305000 Aniruddha Biswas and Palash Sarkar, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL28/Biswas/biswas6.html">Counting Unate and Monotone Boolean Functions Under Restrictions of Balancedness and Non-Degeneracy</a>, J. Int. Seq. (2025) Vol. 28, Art. No. 25.3.4. See pp. 4, 12.
%H A305000 Gus Wiseman, <a href="/A048143/a048143_4.txt">Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons</a>.
%F A305000 Binomial transform of A304999.
%F A305000 Inverse binomial transform of A245079. - _Aniruddha Biswas_, May 11 2024
%e A305000 The a(2) = 8 antichains:
%e A305000   {}
%e A305000   {{1}}
%e A305000   {{2}}
%e A305000   {{1,2}}
%e A305000   {{1},{2}}
%e A305000   {{1},{1,2}}
%e A305000   {{2},{1,2}}
%e A305000   {{1},{2},{1,2}}
%Y A305000 Cf. A006126, A261005, A304996, A304997, A304998, A304999, A305000, A305001.
%Y A305000 Cf. A000372, A003182, A014466, A293606, A293993, A306505, A320449, A321679.
%Y A305000 Cf. A245079.
%K A305000 nonn,more
%O A305000 0,2
%A A305000 _Gus Wiseman_, May 23 2018
%E A305000 a(5)-a(8) from _Gus Wiseman_, May 31 2018
%E A305000 a(9) from _Aniruddha Biswas_, May 11 2024