Non-isomorphic representatives of the a(1) = 1 through a(3) = 9 sets of sets of sets:
{{1}} {{12}} {{123}}
{{1}{2}} {{1}{12}}
{{1}}{{2}} {{1}{23}}
{{1}}{{12}}
{{1}}{{23}}
{{1}{2}{3}}
{{1}}{{1}{2}}
{{1}}{{2}{3}}
{{1}}{{2}}{{3}}
Non-isomorphic representatives of the a(4) = 33 sets of sets of sets:
{{1234}} {{1}{123}} {{1}{2}{12}} {{1}}{{1}{12}}
{{1}{234}} {{12}{13}} {{1}}{{2}{12}}
{{12}{34}} {{1}}{{123}} {{12}}{{1}{2}}
{{1}}{{234}} {{1}{2}{13}} {{1}}{{2}}{{12}}
{{1}{2}{34}} {{12}}{{13}} {{1}}{{2}}{{1}{2}}
{{12}}{{34}} {{1}}{{1}{23}}
{{1}}{{2}{34}} {{1}}{{2}{13}}
{{1}{2}{3}{4}} {{12}}{{1}{3}}
{{12}}{{3}{4}} {{2}}{{1}{13}}
{{1}}{{2}}{{34}} {{1}}{{1}{2}{3}}
{{1}}{{2}{3}{4}} {{1}}{{2}}{{13}}
{{1}{2}}{{3}{4}} {{1}{2}}{{1}{3}}
{{1}}{{2}}{{3}{4}} {{1}}{{2}}{{1}{3}}
{{1}}{{2}}{{3}}{{4}}
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