Question in topology

[3moonlight9]

Is there any formula that gives a relation between the cardinal number of a given set and the number of the topologies that can be taken from this set?

[Moo Of Doom]

You might want to look at A000798 (http://www.research.att.com/~njas/sequences/A000798) and A001930 (http://www.research.att.com/~njas/sequences/A001930) for some references.

[3moonlight9]

Thank you for the suggestion.
Anyway, what I am reading is not really clear.