A225973 Number of union-closed partitions of weight n.

1, 1, 1, 2, 3, 5, 6, 9, 12, 16, 22, 30, 39, 52, 67, 84, 112, 140, 176, 220, 282, 336, 434, 527, 660, 798, 998, 1186, 1480, 1767, 2165, 2586, 3168, 3732, 4556, 5389, 6482, 7654, 9211, 10789, 12937, 15153, 18037, 21086, 25060, 29159, 34527, 40172, 47301, 54927

Offset: 0

Author

Allan C. Wechsler, May 26 2013

Keywords

• nonn

Comments

The objects being counted are sets of sets of positive integers; each such set is closed under set union, and the sum of all the elements of its elements is n.

The sequence is related to Frankl's notorious union-closed sets conjecture, see the Wikipedia link.

Examples

			For n = 5, the a(5) = 5 union-closed partitions are: {{5}}, {{4,1}}, {{3,2}}, {{3,1},{1}}, {{2,1},{2}}.
{{3},{2}} has the correct sum, but is not closed under union.
		

References

• This sequence was proposed by David S. Newman, in a note to the SeqFan mailing list, dated May 19 2013.

Links

• Wikipedia, Union-closed sets conjecture
• David S. Newman, Need help calculating

Crossrefs

Cf. A050342 (answers a similar question without the requirement that the sets be closed under union).