cp's OEIS Frontend

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

%I A056156 #25 Oct 14 2020 23:11:53
%S A056156 1,2,3,7,12,32,67,181,458,1295,3642,10975,33448,106424,345964,1159489,
%T A056156 3975367,13977808,50238606,184629655,692757132,2652892219,10359676617,
%U A056156 41233344350,167171988557,690054189750,2898637406813,12385234548345
%N A056156 Number of connected bipartite graphs with n edges, no isolated vertices and a distinguished bipartite block, up to isomorphism.
%C A056156 EULERi transform of A049311.
%C A056156 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
%H A056156 Jean-François Alcover, <a href="/A056156/b056156.txt">Table of n, a(n) for n = 1..102</a>
%H A056156 Daniel R. Herber, <a href="https://www.engr.colostate.edu/~drherber/files/Herber2020b.pdf">Enhancements to the perfect matching approach for graph enumeration-based engineering challenges</a>, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2020).
%H A056156 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%e A056156 From _Gus Wiseman_, Sep 24 2018: (Start)
%e A056156 Non-isomorphic representatives of the a(1) = 1 through a(4) = 7 connected set multipartitions:
%e A056156   {{1}}   {{1,2}}     {{1,2,3}}      {{1,2,3,4}}
%e A056156          {{1},{1}}   {{2},{1,2}}    {{3},{1,2,3}}
%e A056156                     {{1},{1},{1}}   {{1,2},{1,2}}
%e A056156                                     {{1,3},{2,3}}
%e A056156                                    {{1},{2},{1,2}}
%e A056156                                    {{2},{2},{1,2}}
%e A056156                                   {{1},{1},{1},{1}}
%e A056156 (End)
%t A056156 A049311 = Cases[Import["https://oeis.org/A049311/b049311.txt", "Table"], {_, _}][[All, 2]];
%t A056156 (* EulerInvTransform is defined in A022562 *)
%t A056156 EulerInvTransform[A049311] (* _Jean-François Alcover_, Mar 16 2020 *)
%Y A056156 Cf. A007716, A007718, A056156, A319557, A319565, A319566.
%K A056156 nonn
%O A056156 1,2
%A A056156 _Vladeta Jovovic_, Jul 30 2000
%E A056156 More terms from _Max Alekseyev_, Jul 22 2009