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EXAMPLE
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The a(4) = 11:
{{1,2,3},{1,2,4}}
{{1,2,3},{1,3,4}}
{{1,2,3},{2,3,4}}
{{1,2,4},{1,3,4}}
{{1,2,4},{2,3,4}}
{{1,3,4},{2,3,4}}
{{1,2,3},{1,2,4},{1,3,4}}
{{1,2,3},{1,2,4},{2,3,4}}
{{1,2,3},{1,3,4},{2,3,4}}
{{1,2,4},{1,3,4},{2,3,4}}
{{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
The following are non-isomorphic representatives of the 3 unlabeled 3-uniform hypergraphs spanning 7 vertices with no two edges having exactly one vertex in common, and their multiplicities in the labeled case, which add up to a(7) = 406.
210 X {{1,2,3},{4,6,7},{5,6,7}}
140 X {{1,2,3},{4,5,7},{4,6,7},{5,6,7}}
21 X {{1,6,7},{2,6,7},{3,6,7},{4,6,7},{5,6,7}}
35 X {{1,2,3},{4,5,6},{4,5,7},{4,6,7},{5,6,7}}
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