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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
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
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