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

Author

Gus Wiseman, Sep 27 2018

Keywords

• nonn

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.

Examples

			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}}
		

Links

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

Crossrefs

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

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

Formula

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

Extensions

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