A284762 Total number of subsets of X that are open and closed and connected summed over all distinct topological spaces X that can be placed on an n-set.
1, 2, 9, 69, 852, 16363, 479435, 21150888, 1388124543, 133822887673, 18707633394606, 3745998552621317, 1062675319801676431, 423005074717335908762, 234301896939296139079453, 179277553685814268284430793, 188286118651948743843774496644, 269901723843412313246289232355847, 525443899393186663528068248469425039
Offset: 0
Keywords
Examples
a(2) = 9. Let X = {a,b}. There are four distinct topologies (A000798) that can be placed on X: {{},X} {{},{a},X} {{}, {b},X} {{},{a},{b},X}. These topologies have 2 + 2 + 2 + 3 sets respectively that are open and closed and connected.
Crossrefs
Cf. A281547.
Formula
E.g.f.: (log(A(exp(x)-1))+1)*A(exp(x)-1) where A(x) is the e.g.f. for A001035.