A054951 Number of unlabeled semi-strong digraphs on n nodes with mutually nonisomorphic components.

1, 1, 4, 78, 4960, 1041872, 704369984, 1579641879248, 12137443766888448, 328148810741254606592, 31830752699315833628787200, 11234243165959817684710307801600, 14576241398832991116522929933694031872, 70075699209573863790264288901653500497274880

Offset: 1

Author

N. J. A. Sloane, May 24 2000

Keywords

• nonn
• easy

Comments

A digraph is semi-strong if all its weakly connected components are strongly connected. - Andrew Howroyd, Jan 14 2022

References

• V. A. Liskovets, A contribution to the enumeration of strongly connected digraphs, Dokl. AN BSSR, 17 (1973), 1077-1080 (Russian), MR49#4849.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Crossrefs

Cf. A035512, A049387, A054952, A054953, A054954.

Programs

Mathematica

m = 15;
A035512 = Cases[Import["https://oeis.org/A035512/b035512.txt", "Table"], {, }][[All, 2]];
gf = 1 - Product[(1 - x^n)^A035512[[n + 1]], {n, 1, m}];
CoefficientList[gf + O[x]^m , x] // Rest (* Jean-François Alcover, Aug 26 2019, after Andrew Howroyd *)

Formula

G.f.: 1 - Product_{n > 0} (1 - x^n)^A035512(n). - Andrew Howroyd, Sep 10 2018

Extensions

More terms from Vladeta Jovovic, Mar 11 2003

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