A058338 Number of digraphs with indegree = outdegree at each vertex, or Eulerian digraphs (including disconnected graphs) with n nodes.

1, 1, 2, 5, 18, 111, 2292, 181519, 51294836, 48814342597, 157166848652408, 1736132851915020181, 66689407510956897981608, 9012860249531358132125181323, 4328664025050045497712238253179872, 7451990930474005836163802713084971814275, 46329549163592383403451764167315165130121820112

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

Every regular tournament (A096368) is a Eulerian digraph. Similar methods may be used to compute terms of this sequence. - Andrew Howroyd, Apr 12 2020

References

• F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 219 (but there is an error).
• Ronald C. Read, email to N. J. A. Sloane, 28 August, 2000.

Crossrefs

Cf. A007080 (labeled), A058337 (connected), A096368, A308161, A308111.

Programs

Mathematica

A058337 = Cases[Import["https://oeis.org/A058337/b058337.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A058337] (* Jean-François Alcover, Feb 23 2020, upated Mar 18 2020 *)

Formula

Euler transform of A058337.

Extensions

a(7) added using A058337 by Falk Hüffner, Dec 03 2015

a(8) and a(9) added using A058337 by Brendan McKay, May 05 2019

Terms a(10) and beyond from Andrew Howroyd, Apr 12 2020