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

0,3

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.

Links

Table of n, a(n) for n=0..16.

Formula

Euler transform of A058337.

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 *)

Crossrefs

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

Sequence in context: A007769 A174122 A005805 * A006896 A125625 A281532

Adjacent sequences: A058335 A058336 A058337 * A058339 A058340 A058341

Keyword

nonn,nice

Author

N. J. A. Sloane

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

Status

approved