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EXAMPLE
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G.f. = 1 + x + 4*x^2 + 5*x^3 + 14*x^4 + 18*x^5 + 41*x^6 + 54*x^7 + 109*x^8 + ...
G.f. = q^-5 + q^19 + 4*q^43 + 5*q^67 + 14*q^91 + 18*q^115 + 41*q^139 + ...
Non-isomorphic representatives of the a(1) = 1 through a(5) = 18 multiset partitions using singletons or pairs where no vertex appears more than twice:
{{1}} {{1,1}} {{1},{2,2}} {{1,1},{2,2}} {{1},{2,2},{3,3}}
{{1,2}} {{1},{2,3}} {{1,2},{1,2}} {{1},{2,3},{2,3}}
{{1},{1}} {{2},{1,2}} {{1,2},{3,3}} {{1},{2,3},{4,4}}
{{1},{2}} {{1},{2},{2}} {{1,2},{3,4}} {{1},{2,3},{4,5}}
{{1},{2},{3}} {{1,3},{2,3}} {{1},{2,4},{3,4}}
{{1},{1},{2,2}} {{2},{1,2},{3,3}}
{{1},{1},{2,3}} {{2},{1,3},{2,3}}
{{1},{2},{1,2}} {{4},{1,2},{3,4}}
{{1},{2},{3,3}} {{1},{1},{3},{2,3}}
{{1},{2},{3,4}} {{1},{2},{2},{3,3}}
{{1},{3},{2,3}} {{1},{2},{2},{3,4}}
{{1},{1},{2},{2}} {{1},{2},{3},{2,3}}
{{1},{2},{3},{3}} {{1},{2},{3},{4,4}}
{{1},{2},{3},{4}} {{1},{2},{3},{4,5}}
{{1},{2},{4},{3,4}}
{{1},{2},{2},{3},{3}}
{{1},{2},{3},{4},{4}}
{{1},{2},{3},{4},{5}}
(End)
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