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A056156
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Number of connected bipartite graphs with n edges, no isolated vertices and a distinguished bipartite block, up to isomorphism.
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45
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1, 2, 3, 7, 12, 32, 67, 181, 458, 1295, 3642, 10975, 33448, 106424, 345964, 1159489, 3975367, 13977808, 50238606, 184629655, 692757132, 2652892219, 10359676617, 41233344350, 167171988557, 690054189750, 2898637406813, 12385234548345
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OFFSET
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1,2
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COMMENTS
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Also the number of non-isomorphic connected set multipartitions (multisets of sets) of weight n. The weight of a set multipartition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. - Gus Wiseman, Sep 23 2018
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LINKS
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EXAMPLE
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Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 connected set multipartitions:
{{1}} {{1,2}} {{1,2,3}} {{1,2,3,4}}
{{1},{1}} {{2},{1,2}} {{3},{1,2,3}}
{{1},{1},{1}} {{1,2},{1,2}}
{{1,3},{2,3}}
{{1},{2},{1,2}}
{{2},{2},{1,2}}
{{1},{1},{1},{1}}
(End)
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MATHEMATICA
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A049311 = Cases[Import["https://oeis.org/A049311/b049311.txt", "Table"], {_, _}][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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