%I #24 Feb 20 2023 22:08:38
%S 1,1,2,5,18,111,2292,181519,51294836,48814342597,157166848652408,
%T 1736132851915020181,66689407510956897981608,
%U 9012860249531358132125181323,4328664025050045497712238253179872,7451990930474005836163802713084971814275,46329549163592383403451764167315165130121820112
%N Number of digraphs with indegree = outdegree at each vertex, or Eulerian digraphs (including disconnected graphs) with n nodes.
%C Every regular tournament (A096368) is a Eulerian digraph. Similar methods may be used to compute terms of this sequence. - _Andrew Howroyd_, Apr 12 2020
%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 219 (but there is an error).
%D Ronald C. Read, email to _N. J. A. Sloane_, 28 August, 2000.
%F Euler transform of A058337.
%t A058337 = Cases[Import["https://oeis.org/A058337/b058337.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerTransform is defined in A005195 *)
%t EulerTransform[Rest @ A058337] (* _Jean-François Alcover_, Feb 23 2020, upated Mar 18 2020 *)
%Y Cf. A007080 (labeled), A058337 (connected), A096368, A308161, A308111.
%K nonn,nice
%O 0,3
%A _N. J. A. Sloane_
%E a(7) added using A058337 by _Falk Hüffner_, Dec 03 2015
%E a(8) and a(9) added using A058337 by _Brendan McKay_, May 05 2019
%E Terms a(10) and beyond from _Andrew Howroyd_, Apr 12 2020