[seqfan] Re: A086714

[William Keith]

I will endeavor to explain the value of the comment, as requested.  Why
would one be interested in the series (a(n-1) choose 2) in a graph context?

I would say that the comment makes sense since graphs are very abstract
objects which can describe a multitude of things.  In this case, suppose we
have four objects.  In order to perform some action on them, we need to
consider some binary relations among those objects -- there are six.  But
now we must next account for binary relations among the relations -- there
are 15.  But now we must next account... etc.  And of course in the graph
context these are edges in successive complete graphs on larger numbers of
vertices.

In fact, given this description, I would say that it would also make sense
to create similar sequences starting with 5, etc. (so we get a table), or
to consider triples (i.e., 2-dimensional simplexes), etc.

Does this help?

Best,
William Keith