

A006905


Number of transitive relations on n labeled nodes.
(Formerly M2065)


7



1, 2, 13, 171, 3994, 154303, 9415189, 878222530, 122207703623, 24890747921947, 7307450299510288, 3053521546333103057, 1797003559223770324237, 1476062693867019126073312, 1679239558149570229156802997, 2628225174143857306623695576671, 5626175867513779058707006016592954, 16388270713364863943791979866838296851, 64662720846908542794678859718227127212465
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OFFSET

0,2


REFERENCES

D. Ford and J. McKay, personal communication, 1991.
Klaska (1997), Transitivity and Partial Order, Mathematica Bohemica, 122 (1), 7582. 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).


LINKS

Table of n, a(n) for n=0..18.
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.


FORMULA

E.g.f.: A(x + exp(x)  1) where A(x) is the e.g.f. for A001035.  Geoffrey Critzer, Jul 28 2014


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(ns, ks, 2)))
\\ Charles R Greathouse IV, Sep 05 2011


CROSSREFS

Cf. A000595, A001173. See A091073 for unlabeled case.
Sequence in context: A078363 A143851 A088316 * A119400 A182314 A183606
Adjacent sequences: A006902 A006903 A006904 * A006906 A006907 A006908


KEYWORD

nonn,nice


AUTHOR

Simon Plouffe and N. J. A. Sloane.


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


STATUS

approved



