Is there some known sequence which gives me the number of graphs with diameter d?

Similarly is there some 2D-sequence which gives me the number of graphs with n vertices and diameter d?

If there is no closed form is there some way to study this problem in terms of generating function and apply to it some asymptotic analysis like in "Analytic Combinatorics": http://algo.inria.fr/flajolet/Publications/books.html