[seqfan] intersection patterns of n sets

[Joerg Arndt]

Removing all "geometric" restrictions from
  https://oeis.org/A250001
and changing "circles" to "sets" we get a
comment that could possibly put into some(*)
sequence:

"a(n+1) is the number of intersection patterns
of n (unlabeled) sets of unlabeled elements."


Now which one would be (*)?
Spoiler below.























SPOILER:

Comment goes on:
"Take n nodes for the sets and put an edge between to
sets whenever they have a nonempty intersection;
take one extra node and put an edge to a set whenever
it has an element that is unique to it."


Yes, sequence (*) is
  https://oeis.org/A000088


Is this a comment worthy of being put into A000088 ?

If so, should a similar comment appear in
  https://oeis.org/A001349
?

Best regards,  jj