%I #24 Mar 17 2020 10:16:32
%S 1,2,5,25,157,1325,14358,199763,3549001,80673244,2352747542,
%T 88240542454,4261209044877,264988507673267,21207485269909946,
%U 2182146922863398203
%N a(n) is the number of connected transitive relations over n unlabeled nodes.
%C 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.
%e 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.
%t A091073 = Cases[Import["https://oeis.org/A091073/b091073.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerInvTransform is defined in A022562 *)
%t {1} ~Join~ EulerInvTransform[A091073 // Rest] (* Jean-François Alcover, Dec 29 2019, updated Mar 17 2020 *)
%Y Cf. A091073 (all unlabeled transitive relations). For the labeled case, see A245731 (connected labeled transitive relations) and A006905 (all labeled transitive relations).
%K nonn,more
%O 0,2
%A _Daniele P. Morelli_, Dec 04 2017