A054955 -id:A054955 - cp's OEIS frontend

A054956 Number of labeled Eulerian digraphs with n nodes and an odd number of edges.

0, 0, 2, 64, 3808, 687616, 438948304, 1023160166400, 8829110850999296, 284886609918480818176, 34640035331694391925165824, 15970703846423879100651622752256, 28060860469435555251136195646902620160, 188681219498365676664628141013181314824798208

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. A007080, A054955.

A007080 = Cases[Import["https://oeis.org/A007080/b007080.txt", "Table"], {, }][[All, 2]];
a[n_] := (A007080[[n]] - n!)/2;
Array[a, 14] (* Jean-François Alcover, Aug 27 2019 *)

a(n) = (A007080(n) - n!)/2. - Andrew Howroyd, Sep 10 2018

More terms from Vladeta Jovovic, Mar 05 2001

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

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

A054956 Number of labeled Eulerian digraphs with n nodes and an odd number of edges.

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A054957 Number of labeled connected Eulerian digraphs with n nodes.

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Author

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

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Mathematica

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions