A280192 -id:A280192 - cp's OEIS frontend

A280202 Number of topologies on an n-set X such that for all x in X there is a y in X such that x and y are topologically indistinguishable.

1, 0, 1, 1, 10, 31, 361, 2164, 32663, 313121, 6199024, 86219497, 2225685925, 42396094690, 1414152064833, 35520966967269, 1517860883350266, 48936884016265947, 2659543345912283917, 107827798819822505332, 7409614386025588874195, 371626299919138199117981

Offset: 0

Geoffrey Critzer, Dec 28 2016

nonn

Equivalently a(n) is the number of topologies on an n-set X such that for all x in X there is a y in X such that x and y have exactly the same neighborhoods.

			a(4) = 10 because letting X = {a,b,c,d} we have the trivial topology; {{},{b,c},{a,d},X} * 3; and {{},{a,b},X} *6.

Pontus von Brömssen, Table of n, a(n) for n = 0..37
Wikipedia, Topological indistinguishability.

Column k=0 of A280192.

Cf. A001035, A008299.

E.g.f.: A(exp(x) - 1 - x) where A(x) is the e.g.f. for A001035.

a(n) = Sum_{k=0..floor(n/2)} A008299(n,k)*A001035(k).

a(19)-a(21) from Pontus von Brömssen, Apr 05 2023

cp's OEIS Frontend

A280202 Number of topologies on an n-set X such that for all x in X there is a y in X such that x and y are topologically indistinguishable.

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