A296105 a(n) is the number of connected transitive relations over n unlabeled nodes.

1, 2, 5, 25, 157, 1325, 14358, 199763, 3549001, 80673244, 2352747542, 88240542454, 4261209044877, 264988507673267, 21207485269909946, 2182146922863398203

Offset: 0

Author

Daniele P. Morelli, Dec 04 2017

Keywords

• nonn
• more

Comments

Inverse Euler transform of A091073. Here "connected" means that it is possible to reach any vertex starting from any other vertex by traversing edges in some direction, i.e., not necessarily in the direction in which the edges point, as in weakly connected digraphs.

Examples

			a(2) = 5 because there are five connected transitive relations up to isomorphism: a->b with no loops, a->b with a loop on a, a->b with a loop on b, a->b->a with no loops, and a->b->a with loops on both a and b.
		

Crossrefs

Cf. A091073 (all unlabeled transitive relations). For the labeled case, see A245731 (connected labeled transitive relations) and A006905 (all labeled transitive relations).

Programs

Mathematica

A091073 = Cases[Import["https://oeis.org/A091073/b091073.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
{1} ~Join~ EulerInvTransform[A091073 // Rest] (* Jean-François Alcover, Dec 29 2019, updated Mar 17 2020 *)