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A006058
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Number of connected labeled T_4-topologies with n points.
(Formerly M3030)
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10
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1, 1, 3, 16, 145, 2111, 47624, 1626003, 82564031, 6146805142, 662718022355, 102336213875523, 22408881211102698, 6895949927379360277, 2958271314760111914191, 1756322140048351303019576
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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M. Erne', Struktur- und Anzahlformeln fuer Topologien auf Endlichen Mengen, Manuscripta Math., 11 (1974), 221-259.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008, Table of n, a(n) for n = 0..19
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FORMULA
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a(n) = Sum(k=0..n-1, C(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. - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
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CROSSREFS
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Sequences in the Erne' (1974) paper: A000798, A001035, A006056, A006057, A001929, A001927, A006058, A006059, A000110.
Sequence in context: A020554 A062874 A109398 * A121588 A214933 A230323
Adjacent sequences: A006055 A006056 A006057 * A006059 A006060 A006061
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008
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STATUS
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approved
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