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EXAMPLE
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Non-isomorphic representatives of the a(1) = 1 through a(5) = 17 multiset partitions:
{{1}} {{1,1}} {{1,1,1}} {{1,1,1,1}} {{1,1,1,1,1}}
{{1},{2}} {{1},{2,2}} {{1,1},{2,2}} {{1,1},{1,2,2}}
{{2},{1,2}} {{1,2},{1,2}} {{1,1},{2,2,2}}
{{1},{2},{3}} {{1},{2,2,2}} {{1,2},{1,2,2}}
{{2},{1,2,2}} {{1},{2,2,2,2}}
{{1},{1},{2,3}} {{2},{1,2,2,2}}
{{1},{2},{3,3}} {{1},{2,2},{3,3}}
{{1},{3},{2,3}} {{1},{2,3},{2,3}}
{{1},{2},{3},{4}} {{1},{2},{3,3,3}}
{{1},{3},{2,3,3}}
{{2},{1,2},{3,3}}
{{2},{1,3},{2,3}}
{{3},{3},{1,2,3}}
{{1},{2},{2},{3,4}}
{{1},{2},{3},{4,4}}
{{1},{2},{4},{3,4}}
{{1},{2},{3},{4},{5}}
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