%I #21 Aug 17 2019 15:24:50
%S 1,1,0,1,2,14,964,3908438
%N Number of unlabeled 3-uniform hypergraphs spanning n vertices such that every pair of vertices appears together in some block.
%e Non-isomorphic representatives of the a(5) = 14 hypergraphs:
%e {{123}{145}{245}{345}}
%e {{123}{124}{135}{245}{345}}
%e {{123}{145}{235}{245}{345}}
%e {{123}{134}{145}{235}{245}{345}}
%e {{123}{145}{234}{235}{245}{345}}
%e {{124}{135}{145}{235}{245}{345}}
%e {{125}{135}{145}{235}{245}{345}}
%e {{123}{124}{135}{145}{235}{245}{345}}
%e {{124}{135}{145}{234}{235}{245}{345}}
%e {{125}{135}{145}{234}{235}{245}{345}}
%e {{123}{124}{135}{145}{234}{235}{245}{345}}
%e {{125}{134}{135}{145}{234}{235}{245}{345}}
%e {{124}{125}{134}{135}{145}{234}{235}{245}{345}}
%e {{123}{124}{125}{134}{135}{145}{234}{235}{245}{345}}
%Y The labeled case is A302394.
%Y Cf. A000665, A006126, A006129, A038041, A299471, A301922, A302374, A306021, A320395, A322451.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, Jan 09 2019
%E a(6)-a(7) from _Andrew Howroyd_, Aug 17 2019