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A006056 Number of topologies on n labeled points satisfying the T_4 axiom.
(Formerly M3615)
10
1, 1, 4, 26, 255, 3642, 75606, 2316169, 106289210, 7321773414, 748425136289, 111576624613588, 23864968806932886, 7225895692327786931, 3064182503223082011556, 1803904252801640389374494, 1463405916763710662849541695, 1625522872429294851288338156654 (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, 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)

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

CROSSREFS

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

Sequence in context: A192546 A213438 A056786 * A215242 A098620 A215266

Adjacent sequences:  A006053 A006054 A006055 * A006057 A006058 A006059

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 December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)