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A086366
Number of labeled n-node digraphs in which every node belongs to a directed cycle.
3
1, 0, 1, 18, 1699, 587940, 750744901, 3556390155318, 63740128872703879, 4405426607409460017480, 1190852520892329350092354441, 1270598627613805616203391468226138, 5381238039128882594932248239301142751179, 90766634183072089515270648224715368261615375340
OFFSET
0,4
COMMENTS
These are the directed graphs whose strong components exclude a single vertex. - Andrew Howroyd, Jan 15 2022
PROG
(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
CROSSREFS
Column k=0 of A361592.
The unlabeled version is A361586.
Sequence in context: A160307 A003030 A276016 * A086193 A064347 A253121
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended and terms a(12) and beyond from Andrew Howroyd, Jan 15 2022
STATUS
approved