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Number of digraphs on n labeled nodes with a global source (or sink).
6

%I #11 Jan 22 2022 23:43:09

%S 1,2,24,1216,232960,164069376,428074336256,4220285062479872,

%T 160166476125189439488,23705806454651474422005760,

%U 13794322751716126282614505996288,31714534285699906476309208596247216128,288989543377657933541050197425959169851129856

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

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

%H Andrew Howroyd, <a href="/A350792/b350792.txt">Table of n, a(n) for n = 1..50</a>

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

%o (PARI) InitiallyV(15) \\ See A350793 for program code.

%o (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}

%Y The unlabeled version is A350360.

%Y Row sums of A350793.

%Y Cf. A003025, A003028, A350790.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Jan 16 2022