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%I #16 Dec 17 2022 12:48:34
%S 1,2,2,36,19020,2010231696,9219217412568364176,
%T 170141181796805105960861096082778425120,
%U 57896044618658097536026644159052312977171804852352892309392604715987334365792
%N Number of n-element unlabeled ordered T_0-antichains without isolated vertices; number of T_1-hypergraphs (without empty edge and without multiple edges) on n labeled vertices.
%H V. Jovovic, <a href="/A059523/a059523.pdf">T_1-hyper graphs on a labeled 3-set</a>
%H Goran Kilibarda and Vladeta Jovovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL7/Kilibarda/kili2.html">Antichains of Multisets</a>, J. Integer Seqs., Vol. 7, 2004.
%H Goran Kilibarda and Vladeta Jovovic, <a href="https://arxiv.org/abs/1411.4187">Enumeration of some classes of T_0-hypergraphs</a>, arXiv:1411.4187 [math.CO], 2014.
%F a(n) = A059052(n)/2.
%e Number of k-element T_1-hipergraphs (without empty edge and without multiple edges) on 3 labeled vertices is
%e C(7,k)-6*C(5,k)+6*C(4,k)+3*C(3,k)-6*C(2,k)+2*C(1,k),k=0..7; so a(3)=2+11+15+7+1=36=2^7-6*2^5+6*2^4+3*2^3-6*2^2+2*2.
%Y Cf. A003465, A059201, A059052, A326961.
%K nonn
%O 0,2
%A _Vladeta Jovovic_ and Goran Kilibarda, Jan 20 2001; revised Jun 03 2004
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