A058337 -id:A058337 - cp's OEIS frontend

A039750 Erroneous version of A058337.

1, 1, 1, 3, 12, 68

Offset: 0

dead

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 219.

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

N. J. A. Sloane

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

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.

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

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 *)

Euler transform of A058337.

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

A054957 Number of labeled connected Eulerian digraphs with n nodes.

Original entry on oeis.org

1, 1, 6, 118, 7000, 1329496, 868255024, 2039295163312, 17639804273910144, 569596637165777524096, 69273803156588266525129984, 31940576331984155835757999795456, 56121305700570450429977355284230355968, 377361653292638108206937443603065676106341376

Offset: 1

N. J. A. Sloane, May 24 2000

Alois P. Heinz, Table of n, a(n) for n = 1..16
V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Cf. A058338, A054955, A007080 (EXP-transform), A054959, A054956, A058337, A054958.

a(n) = A054958(n) + A054959(n). - R. J. Mathar, Apr 13 2017

More terms from Vladeta Jovovic, Mar 06 2001

More terms from Alois P. Heinz, Apr 14 2017

A054958 Number of labeled connected Eulerian digraphs with n nodes and an even number of edges.

Original entry on oeis.org

1, 1, 4, 62, 3512, 664808, 434127872, 1019647584176, 8819902136975232, 284798318582888943488, 34636901578294133264379392, 15970288165992077917879019856128, 28060652850285225214988677642354678784, 188680826646319054103468721801532841166681088

Offset: 1

N. J. A. Sloane, May 24 2000

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Cf. A058338, A054955, A007080, A054959, A054956, A058337, A054957.

A054957 = Cases[Import["https://oeis.org/A054957/b054957.txt", "Table"], {, }][[All, 2]];
a[n_] := (A054957[[n]] + (n - 1)!)/2;
Array[a, 14] (* Jean-François Alcover, Sep 13 2019 *)

a(n) = (A054957 + (n-1)!)/2. - Andrew Howroyd, Sep 10 2018

More terms from Vladeta Jovovic, Mar 06 2001

a(12)-a(14) from Andrew Howroyd, Sep 10 2018

A054959 Number of labeled connected Eulerian digraphs with n nodes and an odd number of edges.

Original entry on oeis.org

0, 0, 2, 56, 3488, 664688, 434127152, 1019647579136, 8819902136934912, 284798318582888580608, 34636901578294133260750592, 15970288165992077917878979939328, 28060652850285225214988677641875677184, 188680826646319054103468721801532834939660288

Offset: 1

N. J. A. Sloane, May 24 2000

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Cf. A058338, A054955, A007080, A054956, A058337, A054958, A054957.

A054957 = Cases[Import["https://oeis.org/A054957/b054957.txt", "Table"], {, }][[All, 2]];
a[n_] := (A054957[[n]] - (n - 1)!)/2;
Array[a, 14] (* Jean-François Alcover, Sep 13 2019 *)

a(n) = (A054957(n) - (n-1)!)/2. - Andrew Howroyd, Sep 10 2018

More terms from Vladeta Jovovic, Mar 06 2001

a(12)-a(14) from Andrew Howroyd, Sep 10 2018

cp's OEIS Frontend

A039750 Erroneous version of A058337.

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

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A054957 Number of labeled connected Eulerian digraphs with n nodes.

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Formula

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A054958 Number of labeled connected Eulerian digraphs with n nodes and an even number of edges.

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Programs

Mathematica

Formula

Extensions

A054959 Number of labeled connected Eulerian digraphs with n nodes and an odd number of edges.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions