A350792 Number of digraphs on n labeled nodes with a global source (or sink).

1, 2, 24, 1216, 232960, 164069376, 428074336256, 4220285062479872, 160166476125189439488, 23705806454651474422005760, 13794322751716126282614505996288, 31714534285699906476309208596247216128, 288989543377657933541050197425959169851129856

Offset: 1

Author

Andrew Howroyd, Jan 16 2022

Keywords

• nonn

Comments

A global sink is a node that has out-degree zero and to which all other nodes have a directed path.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50

Crossrefs

The unlabeled version is A350360.

Row sums of A350793.

Cf. A003025, A003028, A350790.

Programs

PARI

InitiallyV(15) \\ See A350793 for program code.

PARI

seq(n)={my(v=vector(n)); for(n=1, n, v[n] = n*2^((n-1)^2) - sum(k=1, n-1, binomial(n,k)*2^((n-2)*(n-k))*v[k])); v}

Formula

a(n) = n*2^((n-1)^2) - Sum_{k=1..n-1} binomial(n,k)*2^((n-2)*(n-k))*a(k).