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Number of labeled antichains of finite sets spanning some subset of {1,...,n} with singleton edges allowed.
23

%I #29 May 11 2024 17:03:38

%S 1,2,8,72,1824,220608,498243968,309072306743552,

%T 14369391925598802012151296,

%U 146629927766168786239127150948525247729660416

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

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

%C Number of non-degenerate unate Boolean functions of n or fewer variables. - _Aniruddha Biswas_, May 11 2024

%H A. Biswas and P. Sarkar, <a href="https://arxiv.org/abs/2304.14069">Counting unate and balanced monotone Boolean functions,</a> arXiv:2304.14069 [math.CO], 2023.

%H 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 Binomial transform of A304999.

%F Inverse binomial transform of A245079. - _Aniruddha Biswas_, May 11 2024

%e The a(2) = 8 antichains:

%e {}

%e {{1}}

%e {{2}}

%e {{1,2}}

%e {{1},{2}}

%e {{1},{1,2}}

%e {{2},{1,2}}

%e {{1},{2},{1,2}}

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

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

%Y Cf. A245079.

%K nonn,more

%O 0,2

%A _Gus Wiseman_, May 23 2018

%E a(5)-a(8) from _Gus Wiseman_, May 31 2018

%E a(9) from _Aniruddha Biswas_, May 11 2024