Formulas for Cardinality & Topology of a Set

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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?
 
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You might want to look at http://www.research.att.com/~njas/sequences/A000798 for some references.
 
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Thank you for the suggestion.
Anyway, what I am reading is not really clear.
 

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