A003028 Number of digraphs on n labeled nodes with a source.

1, 3, 51, 3614, 991930, 1051469032, 4366988803688, 71895397383029040, 4719082081411731363408, 1237678715644664931691596416, 1297992266840866792981316221144960, 5444416466164313011147841248189209354496, 91343356480627224177654291875698256656613808896

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

Here a source is a node that is connected by a directed path to every other node in the digraph (but does not necessarily have indegree zero). - Geoffrey Critzer, Apr 14 2023

References

• V. Jovovic and G. Kilibarda, Enumeration of labeled initially-finally connected digraphs, Scientific review, Serbian Scientific Society, 19-20 (1996) 237-247.
• R. W. Robinson, Counting labeled acyclic digraphs, pp. 239-273 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• V. Jovovic and G. Kilibarda, Enumeration of labeled quasi-initially connected digraphs, Discrete Math., 224 (2000), 151-163.

Crossrefs

The unlabeled version is A051421.

Row sums of A057274.

Column k=1 of A361579.

Cf. A003027, A003029, A003030, A049524, A049414, A350792.

Programs

PARI

Initially(12) \\ See A057274. - Andrew Howroyd, Jan 11 2022

Extensions

Corrected and extended by Vladeta Jovovic, Goran Kilibarda

Terms a(12) and beyond from Andrew Howroyd, Jan 11 2022