A319791 Number of non-isomorphic connected set multipartitions (multisets of sets) of weight n with empty intersection.

1, 0, 0, 0, 1, 3, 14, 38, 125, 360, 1107, 3297, 10292, 32134, 103759, 340566, 1148150, 3951339, 13925330, 50122316, 184365292, 692145409, 2651444318, 10356184440, 41224744182, 167150406897, 689998967755, 2898493498253, 12384852601731, 53804601888559, 237566072006014

Offset

0,6

Comments

The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Formula

a(n) = A056156(n) - A049311(n) + A319748(n). - Andrew Howroyd, May 31 2023

Example

Non-isomorphic representatives of the a(4) = 1 through a(6) = 14 set multipartitions:
4:    {{1},{2},{1,2}}
5:   {{2},{3},{1,2,3}}
     {{2},{1,3},{2,3}}
    {{1},{2},{2},{1,2}}
6:  {{1},{1,4},{2,3,4}}
    {{1},{2,3},{1,2,3}}
    {{3},{4},{1,2,3,4}}
    {{3},{1,4},{2,3,4}}
    {{1,2},{1,3},{2,3}}
    {{1,3},{2,4},{3,4}}
   {{1},{2},{3},{1,2,3}}
   {{1},{2},{1,2},{1,2}}
   {{1},{2},{1,3},{2,3}}
   {{2},{2},{1,3},{2,3}}
   {{2},{3},{3},{1,2,3}}
   {{2},{3},{1,3},{2,3}}
  {{1},{1},{2},{2},{1,2}}
  {{1},{2},{2},{2},{1,2}}

Crossrefs

Cf. A007716, A007718, A049311, A056156, A281116, A283877, A317752, A317755, A317757.

Cf. A319077, A319748, A319755, A319778, A319781, A319790.

Sequence in context: A141129 A143941 A162147 * A027444 A000263 A333293

Adjacent sequences: A319788 A319789 A319790 * A319792 A319793 A319794

Keyword

nonn

Author

Gus Wiseman, Sep 27 2018

Extensions

Terms a(11) and beyond from Andrew Howroyd, May 31 2023

Status

approved