OFFSET
0,4
COMMENTS
Digraphs counted here must be loopless, but not necessarily connected.
The definition is not strictly saying that there is no (global) source or sink, because the graphs are counted without considering (strong or weak) connectivity.
(The weakly connected digraphs of this type start 1,0,1,5,89,5327,...)
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
R. J. Mathar, Illustrations (2023), 335 pages
EXAMPLE
From Andrew Howroyd, Jan 02 2024: (Start)
Example of a digraph counted by this sequence but not by A361586:
o <---> o ----> o ----> o <---> o
In the above example, the 3rd vertex has both an in arc and an out arc, but is not part of any directed cycle. (End)
PROG
(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
K(q, t)={sum(j=1, #q, gcd(t, q[j]))}
a(n) = {if(n==0, 1, sum(k=1, n, my(s=0, m=n-k); forpart(p=k, s += permcount(p) * prod(i=1, #p, 2^(K(p, p[i])-1)-1) * polcoef(exp(sum(t=1, m, (1-2^K(p, t))/t*x^t) + O(x*x^m)), m)); s/k!))} \\ Andrew Howroyd, Jan 02 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Nov 20 2023
EXTENSIONS
Terms a(6) and beyond from Andrew Howroyd, Jan 02 2024
STATUS
approved