A006056 Number of topologies on n labeled points satisfying the T_4 axiom.

1, 1, 4, 26, 255, 3642, 75606, 2316169, 106289210, 7321773414, 748425136289, 111576624613588, 23864968806932886, 7225895692327786931, 3064182503223082011556, 1803904252801640389374494, 1463405916763710662849541695, 1625522872429294851288338156654

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Herman Jamke, Table of n, a(n) for n = 0..19
• 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)

Crossrefs

Sequences in the Erné (1974) paper: A000798, A001035, A006056, A006057, A001929, A001927, A006058, A006059, A000110.

Formula

E.g.f.: A4(X) = exp(Z4(X)-1) where Z4(x) denotes the e.g.f. for A006058. - Herman Jamke, 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