login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006057 Number of topologies on n labeled points satisfying axioms T_0-T_4.
(Formerly M3028)
13
1, 1, 3, 16, 137, 1826, 37777, 1214256, 60075185, 4484316358, 493489876721, 78456654767756, 17735173202222665, 5630684018989523274, 2486496790249207981169, 1515191575312017416011456 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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.
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
CROSSREFS
Sequences in the Erné (1974) paper: A000798, A001035, A006056, A006057, A001929, A001927, A006058, A006059, A000110.
Sequence in context: A345349 A230320 A230318 * A305472 A002719 A020554
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
More precise definition from N. J. A. Sloane, Jan 09 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 03:27 EDT 2024. Contains 370952 sequences. (Running on oeis4.)