Non-isomorphic representatives of the a(0) = 2 through a(3) = 28 sets of sets:
{} {{1}} {{12}} {{123}}
{{}} {{}{1}} {{}{12}} {{}{123}}
{{2}{12}} {{3}{123}}
{{}{2}{12}} {{23}{123}}
{{1}{2}{12}} {{}{3}{123}}
{{}{1}{2}{12}} {{}{23}{123}}
{{1}{23}{123}}
{{3}{23}{123}}
{{13}{23}{123}}
{{}{1}{23}{123}}
{{}{3}{23}{123}}
{{}{13}{23}{123}}
{{2}{3}{23}{123}}
{{2}{13}{23}{123}}
{{3}{13}{23}{123}}
{{12}{13}{23}{123}}
{{}{2}{3}{23}{123}}
{{}{2}{13}{23}{123}}
{{}{3}{13}{23}{123}}
{{}{12}{13}{23}{123}}
{{2}{3}{13}{23}{123}}
{{3}{12}{13}{23}{123}}
{{}{2}{3}{13}{23}{123}}
{{}{3}{12}{13}{23}{123}}
{{2}{3}{12}{13}{23}{123}}
{{}{2}{3}{12}{13}{23}{123}}
{{1}{2}{3}{12}{13}{23}{123}}
{{}{1}{2}{3}{12}{13}{23}{123}}
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