[Sloane's encyclopedia][1] gives some references. I think that if something moves in this question, then Sloane's site will be one of the first to be updated...

I am not sure in how far this has to do the Union-Closed Sets Conjecture - the latter is just an extremal-combinatorics style assertion. I don't see how to use it for an enumeration.


  [1]: http://oeis.org/A000798