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Also the number of non-isomorphic set multipartitions (multisets of sets) of weight n where every vertex is the unique common element of some subset of the edges. For example, the a(1) = 1 through a(56) = 9 20 set multipartitions are:

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From Gus Wiseman, Aug 15 2019: (Start)

Also the number of non-isomorphic set multipartitions (multisets of sets) of weight n where every vertex is the unique common element of some subset of the edges. For example, the a(1) = 1 through a(5) = 9 set multipartitions are:

{1} {1}{1} {1}{1}{1} {1}{2}{12} {1}{2}{2}{12} {12}{13}{23}

{1}{2} {1}{2}{2} {1}{1}{1}{1} {1}{2}{3}{23} {1}{2}{12}{12}

{1}{2}{3} {1}{1}{2}{2} {1}{1}{1}{1}{1} {1}{2}{13}{23}

{1}{2}{2}{2} {1}{1}{2}{2}{2} {1}{2}{3}{123}

{1}{2}{3}{3} {1}{2}{2}{2}{2} {1}{1}{2}{2}{12}

{1}{2}{3}{4} {1}{2}{2}{3}{3} {1}{1}{2}{3}{23}

{1}{2}{3}{3}{3} {1}{2}{2}{2}{12}

{1}{2}{3}{4}{4} {1}{2}{3}{3}{23}

{1}{2}{3}{4}{5} {1}{2}{3}{4}{34}

{1}{1}{1}{1}{1}{1}

{1}{1}{1}{2}{2}{2}

{1}{1}{2}{2}{2}{2}

{1}{1}{2}{2}{3}{3}

{1}{2}{2}{2}{2}{2}

{1}{2}{2}{3}{3}{3}

{1}{2}{3}{3}{3}{3}

{1}{2}{3}{3}{4}{4}

{1}{2}{3}{4}{4}{4}

{1}{2}{3}{4}{5}{5}

{1}{2}{3}{4}{5}{6}

(End)

Cf. A000372, A000612, A003182, A014466, A055621, A293993, A326704, A326972.

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Cf. A006126, A006602, A007411, A007716, A048143, A049311, A283877, A293607.

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