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A006905
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Number of transitive relations on n labeled nodes.
(Formerly M2065)
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5
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1, 2, 13, 171, 3994, 154303, 9415189, 878222530, 122207703623, 24890747921947, 7307450299510288, 3053521546333103057, 1797003559223770324237, 1476062693867019126073312, 1679239558149570229156802997, 2628225174143857306623695576671, 5626175867513779058707006016592954, 16388270713364863943791979866838296851, 64662720846908542794678859718227127212465
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| D. Ford and J. McKay, personal communication, 1991.
Klaska (1997), Transitivity and Partial Order, Mathematica Bohemica, 122 (1), 75-82. Based on a correspondence between transitive relations and partial orders, the author obtains a formula and calculates the first 14 terms - Jeff McSweeney (jmcsween(AT)mtsu.edu), May 13, 2000
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. R. Finch, Transitive relations, topologies and partial orders
G. Pfeiffer, Counting Transitive Relations, Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.2.
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PROG
| (PARI) \\ P = [1, 1, 3, 19, ...] is A001035, starting from 0.
a(n)=sum(k=0, n, P[k+1]*sum(s=0, k, binomial(n, s)*stirling(n-s, k-s, 2)))
\\ Charles R Greathouse IV, Sep 05 2011
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CROSSREFS
| Cf. A000595, A001173. See A091073 for unlabeled case.
Sequence in context: A078363 A143851 A088316 * A119400 A183606 A137610
Adjacent sequences: A006902 A006903 A006904 * A006906 A006907 A006908
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KEYWORD
| nonn,nice
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AUTHOR
| Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 28 2003
a(15)-a(16) from Charles R. Greathouse IV Aug 30 2006
a(17)-a(18) from Charles R Greathouse IV, Sep 05 2011
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