A058337 Number of connected loop-free Eulerian digraphs with n nodes.

1, 1, 1, 3, 12, 90, 2162, 179098, 51110788, 48762860958, 157117982629089, 1735975636147643118, 66687671220840028265672, 9012793558387399546070260538, 4328655012123103085159161399497333, 7451986601800967792474321528025564017244, 46329541711597124247394557123740768918978380463

Offset

0,4

Comments

Parallel edges are not allowed, but 2-cycles are allowed. Since these digraphs have an Eulerian circuit, being weakly-connected is the same as being strongly-connected. - Brendan McKay, Apr 04 2023

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.

Eric Weisstein's World of Mathematics, Eulerian Graph

Formula

Inverse Euler transform of A058338. - Andrew Howroyd, Apr 12 2020

Crossrefs

Cf. A058338.

Sequence in context: A366733 A305870 A342395 * A025503 A363254 A368454

Adjacent sequences: A058334 A058335 A058336 * A058338 A058339 A058340

Keyword

nonn,nice,hard

Author

N. J. A. Sloane

Extensions

a(7) (generated graphs with nauty, filtered and counted with Python) by Pietro Battiston, Feb 08 2014

a(8) and a(9) added and description clarified by Brendan McKay, May 05 2019

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

Status

approved