Basic graph counting sequences

[David Wilson]

My sequence S = (1,1,2,4,11,...) is probably best described as simply 
"graphs with n nodes". It is A002494 permitting isolated vertices. If we 
prepend the technically correct A002494(0) = 1, I believe S is then the 
running sum of A002494.

My sequence T = (1,1,1,2,6,...) is sequence of connected graphs with n 
nodes (n >= 0), identified by Eric W. as T = A001349.

I suppose we could then consider the disconnected graphs on n nodes = S 
- T if it is not already there.

It might also be interesting to try to compute sequences C_k = the 
number of n-node graphs with k components, for small k. This would seem 
to me computable from the known sequences.