A006057 Number of topologies on n labeled points satisfying axioms T_0-T_4.
1, 1, 3, 16, 137, 1826, 37777, 1214256, 60075185, 4484316358, 493489876721, 78456654767756, 17735173202222665, 5630684018989523274, 2486496790249207981169, 1515191575312017416011456
Offset: 0
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008, Table of n, a(n) for n = 0..19
- P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
- M. Erné, Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen, Manuscripta Math., 11 (1974), 221-259.
- M. Erné, Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen, Manuscripta Math., 11 (1974), 221-259. (Annotated scanned copy)
- Messaoud Kolli, Direct and Elementary Approach to Enumerate Topologies on a Finite Set, J. Integer Sequences, Volume 10, 2007, Article 07.3.1.
- M. Kolli, On the cardinality of the T_0-topologies on a finite set, International Journal of Combinatorics, Volume 2014 (2014), Article ID 798074, 7 pages.
Crossrefs
Formula
E.g.f.: A04(x)=exp(Z04(x)-1) where Z04(x) denotes the E.g.f. for A006059. - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
Extensions
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
More precise definition from N. J. A. Sloane, Jan 09 2014