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A006058 Number of connected labeled T_4-topologies with n points.
(Formerly M3030)
10
1, 1, 3, 16, 145, 2111, 47624, 1626003, 82564031, 6146805142, 662718022355, 102336213875523, 22408881211102698, 6895949927379360277, 2958271314760111914191, 1756322140048351303019576 (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

From Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008: (Start)

a(n) = Sum_{k=0..n-1} binomial(n, k)*A000798(k) if n>=1.

E.g.f.: Z4(x) = A(x)*(exp(x)-1) + 1 where A(x) denotes the e.g.f. for A000798. (End)

CROSSREFS

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

Sequence in context: A062874 A109398 A294003 * A121588 A264660 A214933

Adjacent sequences:  A006055 A006056 A006057 * A006059 A006060 A006061

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008

STATUS

approved

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Last modified October 22 12:22 EDT 2018. Contains 316446 sequences. (Running on oeis4.)