A086366 Number of labeled n-node digraphs in which every node belongs to a directed cycle.

1, 0, 1, 18, 1699, 587940, 750744901, 3556390155318, 63740128872703879, 4405426607409460017480, 1190852520892329350092354441, 1270598627613805616203391468226138, 5381238039128882594932248239301142751179, 90766634183072089515270648224715368261615375340

Offset: 0

Author

Valery A. Liskovets and Vladeta Jovovic, Sep 04 2003

Keywords

• nonn

Comments

These are the directed graphs whose strong components exclude a single vertex. - Andrew Howroyd, Jan 15 2022

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• Valery Liskovets, Labeled digraphs in which every node belongs to a directed cycle [Broken link]

Crossrefs

Column k=0 of A361592.

The unlabeled version is A361586.

Cf. A003030, A086193.

Programs

PARI

G(p)={my(n=serprec(p,x)); serconvol(p, sum(k=0, n-1, x^k/2^(k*(k-1)/2), O(x^n)))}
U(p)={my(n=serprec(p,x)); serconvol(p, sum(k=0, n-1, x^k*2^(k*(k-1)/2), O(x^n)))}
DigraphEgf(n)={sum(k=0, n, 2^(k*(k-1))*x^k/k!, O(x*x^n) )}
seq(n)={Vec(serlaplace(U(1/G(exp(x+log(U(1/G(DigraphEgf(n)))))))))} \\ Andrew Howroyd, Jan 15 2022

Extensions

a(0)=1 prepended and terms a(12) and beyond from Andrew Howroyd, Jan 15 2022