A003028 Number of digraphs on n labeled nodes with a source. (Formerly M3157)

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

Offset

1,2

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.

Prog

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

Crossrefs

The unlabeled version is A051421.

Row sums of A057274.

Column k=1 of A361579.

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

Sequence in context: A172434 A210676 A105639 * A069343 A084882 A275798

Adjacent sequences: A003025 A003026 A003027 * A003029 A003030 A003031

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

Corrected and extended by Vladeta Jovovic, Goran Kilibarda

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

Status

approved