cp's OEIS Frontend

A006057 Number of topologies on n labeled points satisfying axioms T_0-T_4.

%I A006057 M3028 #37 Apr 08 2019 03:48:12
%S A006057 1,1,3,16,137,1826,37777,1214256,60075185,4484316358,493489876721,
%T A006057 78456654767756,17735173202222665,5630684018989523274,
%U A006057 2486496790249207981169,1515191575312017416011456
%N A006057 Number of topologies on n labeled points satisfying axioms T_0-T_4.
%D A006057 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006057 Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008, <a href="/A006057/b006057.txt">Table of n, a(n) for n = 0..19</a>
%H A006057 P. J. Cameron, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H A006057 M. Erné, <a href="http://dx.doi.org/10.1007/BF01173716">Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen</a>, Manuscripta Math., 11 (1974), 221-259.
%H A006057 M. Erné, <a href="/A006056/a006056.pdf">Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen</a>, Manuscripta Math., 11 (1974), 221-259. (Annotated scanned copy)
%H A006057 Messaoud Kolli, <a href="http://www.emis.de/journals/JIS/VOL10/Kolli/messaoud30.html">Direct and Elementary Approach to Enumerate Topologies on a Finite Set</a>, J. Integer Sequences, Volume 10, 2007, Article 07.3.1.
%H A006057 M. Kolli, <a href="http://dx.doi.org/10.1155/2014/798074">On the cardinality of the T_0-topologies on a finite set</a>, International Journal of Combinatorics, Volume 2014 (2014), Article ID 798074, 7 pages.
%F A006057 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
%Y A006057 Sequences in the Erné (1974) paper: A000798, A001035, A006056, A006057, A001929, A001927, A006058, A006059, A000110.
%K A006057 nonn,nice
%O A006057 0,3
%A A006057 _N. J. A. Sloane_
%E A006057 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
%E A006057 More precise definition from _N. J. A. Sloane_, Jan 09 2014