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

%I A086366 #18 Mar 30 2023 01:58:35
%S A086366 1,0,1,18,1699,587940,750744901,3556390155318,63740128872703879,
%T A086366 4405426607409460017480,1190852520892329350092354441,
%U A086366 1270598627613805616203391468226138,5381238039128882594932248239301142751179,90766634183072089515270648224715368261615375340
%N A086366 Number of labeled n-node digraphs in which every node belongs to a directed cycle.
%C A086366 These are the directed graphs whose strong components exclude a single vertex. - _Andrew Howroyd_, Jan 15 2022
%H A086366 Andrew Howroyd, <a href="/A086366/b086366.txt">Table of n, a(n) for n = 0..50</a>
%H A086366 Valery Liskovets, <a href="http://mathforum.org/epigone/sci.math.research/clangshedi/y02wwhkqdu36&amp;#064;legacy">Labeled digraphs in which every node belongs to a directed cycle</a> [Broken link]
%o A086366 (PARI)
%o A086366 G(p)={my(n=serprec(p,x)); serconvol(p, sum(k=0, n-1, x^k/2^(k*(k-1)/2), O(x^n)))}
%o A086366 U(p)={my(n=serprec(p,x)); serconvol(p, sum(k=0, n-1, x^k*2^(k*(k-1)/2), O(x^n)))}
%o A086366 DigraphEgf(n)={sum(k=0, n, 2^(k*(k-1))*x^k/k!, O(x*x^n) )}
%o A086366 seq(n)={Vec(serlaplace(U(1/G(exp(x+log(U(1/G(DigraphEgf(n)))))))))} \\ _Andrew Howroyd_, Jan 15 2022
%Y A086366 Column k=0 of A361592.
%Y A086366 The unlabeled version is A361586.
%Y A086366 Cf. A003030, A086193.
%K A086366 nonn
%O A086366 0,4
%A A086366 _Valery A. Liskovets_ and _Vladeta Jovovic_, Sep 04 2003
%E A086366 a(0)=1 prepended and terms a(12) and beyond from _Andrew Howroyd_, Jan 15 2022