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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 (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: A135746 A230320 A230318 * A305472 A002719 A020554

Adjacent sequences:  A006054 A006055 A006056 * A006058 A006059 A006060

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

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

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Last modified October 16 10:09 EDT 2018. Contains 316262 sequences. (Running on oeis4.)