Non-isomorphic representatives of the a(5) = 3, a(7) = 14, and a(8) = 13 multiset partitions:
{{11}{122}} {{111}{1222}} {{111}{11222}}
{{11}{222}} {{111}{2222}} {{111}{22222}}
{{12}{122}} {{112}{1222}} {{112}{12222}}
{{11}{22222}} {{122}{11222}}
{{12}{12222}} {{11}{122}{233}}
{{122}{1122}} {{11}{122}{333}}
{{22}{11222}} {{11}{222}{333}}
{{11}{12}{233}} {{11}{223}{233}}
{{11}{22}{233}} {{12}{122}{333}}
{{11}{22}{333}} {{12}{123}{233}}
{{11}{23}{233}} {{13}{112}{233}}
{{12}{12}{333}} {{13}{122}{233}}
{{12}{13}{233}} {{23}{123}{123}}
{{13}{23}{123}}
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