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

0,5

Comments

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.

Links

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

Wikipedia, Topological indistinguishability.

Formula

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).

Example

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.

Crossrefs

Column k=0 of A280192.

Cf. A001035, A008299.

Sequence in context: A042849 A097236 A332254 * A061485 A136335 A008422

Adjacent sequences: A280199 A280200 A280201 * A280203 A280204 A280205

Keyword

nonn

Author

Geoffrey Critzer, Dec 28 2016

Extensions

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

Status

approved