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EXAMPLE
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The a(1) = 1 through a(3) = 8 set multipartitions:
{{1}} {{1,2}} {{1,2,3}}
{{1},{1}} {{1},{1,2}}
{{1},{2}} {{1},{2,3}}
{{2},{1,3}}
{{3},{1,2}}
{{1},{1},{1}}
{{1},{1},{2}}
{{1},{2},{3}}
The a(4) = 27 set multipartitions:
{{1},{1},{1},{1}} {{1},{1},{1,2}} {{1},{1,2,3}} {{1,2,3,4}}
{{1},{1},{1},{2}} {{1},{1},{2,3}} {{1,2},{1,2}}
{{1},{1},{2},{2}} {{1},{2},{1,2}} {{1,2},{1,3}}
{{1},{1},{2},{3}} {{1},{2},{1,3}} {{1},{2,3,4}}
{{1},{2},{3},{4}} {{1},{2},{3,4}} {{1,2},{3,4}}
{{1},{3},{1,2}} {{1,3},{2,4}}
{{1},{3},{2,4}} {{1,4},{2,3}}
{{1},{4},{2,3}} {{2},{1,3,4}}
{{2},{3},{1,4}} {{3},{1,2,4}}
{{2},{4},{1,3}} {{4},{1,2,3}}
{{3},{4},{1,2}}
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