OFFSET
0,4
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.
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
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Allan C. Wechsler, May 26 2013
STATUS
approved