A056156 Number of connected bipartite graphs with n edges, no isolated vertices and a distinguished bipartite block, up to isomorphism.

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

Offset: 1

Author

Vladeta Jovovic, Jul 30 2000

Keywords

• nonn

Comments

EULERi transform of A049311.

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

Examples

			From _Gus Wiseman_, Sep 24 2018: (Start)
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)
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..102
• Daniel R. Herber, Enhancements to the perfect matching approach for graph enumeration-based engineering challenges, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2020).
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A007716, A007718, A056156, A319557, A319565, A319566.

Programs

Mathematica

A049311 = Cases[Import["https://oeis.org/A049311/b049311.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A049311] (* Jean-François Alcover, Mar 16 2020 *)

Extensions

More terms from Max Alekseyev, Jul 22 2009