A085628 - OEIS

%I #13 Jan 01 2020 04:20:59

%S 1,2,12,152,3504,135392,8321472,784621952,110521185024,22789653765632,

%T 6769730814753792,2859584874712881152,1699286839524775931904,

%U 1407801166901961190203392,1613567168628788544015286272,2541721059997800475952740401152,5470980000021882982488097199161344

%N Number of antisymmetric transitive binary relations on n labeled points.

%H Jean-François Alcover, <a href="/A085628/b085628.txt">Table of n, a(n) for n = 0..18</a>

%H G. Pfeiffer, <a href="http://schmidt.nuigalway.ie/~goetz/pub/posetseq.html">Counting Transitive Relations</a>, preprint, 2004.

%F a(n) = 2^n * A001035(n) = A000079(n) * A001035(n)

%F E.g.f.: A(2*x) where A(x) is the e.g.f. for A001035. - _Geoffrey Critzer_, Jul 28 2014

%t A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := 2^n A001035[[n + 1]];

%t a /@ Range[0, 18] (* _Jean-François Alcover_, Jan 01 2020 *)

%Y Cf. A079265 (unlabeled antisymmetric transitive relations), A001035 (labeled partial orders), A000798 (labeled reflexive transitive relations), A006905 (labeled transitive relations).

%K nonn

%O 0,2

%A Goetz Pfeiffer (goetz.pfeiffer(AT)nuigalway.ie), Jan 21 2004

%E 2 more terms from _Charles R Greathouse IV_, Aug 31 2006