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%I #32 Oct 08 2023 08:52:08
%S 1,1,2,22,1688,573496,738218192,3528260038192,63547436065854848,
%T 4400982906402148836736,1190477715153930158152163072,
%U 1270476960212865235273469079407872,5381083212549793228422395071641588743168,90765858793484859057065439213726376149311958016
%N Number of labeled semi-strong digraphs on n nodes.
%C A digraph is semi-strong if all its weakly connected components are strongly connected. - _Andrew Howroyd_, Jan 14 2022
%C A digraph is semi-strong iff the following implication holds for all x,y in [n]: If there is a directed path from x to y then x and y are in the same strongly connected component. - _Geoffrey Critzer_, Oct 07 2023
%H Andrew Howroyd, <a href="/A054948/b054948.txt">Table of n, a(n) for n = 0..50</a>
%H V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LISK/Derseq.html">Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), #00.2.2.
%F E.g.f.: 1/(1-B(x)) where B(x) is e.g.f. for A054947. - _Vladeta Jovovic_, Mar 11 2003
%F E.g.f. A(x) satisfies: Sum_{n>=0} 2^(n^2-n)*x^n/n! / A(2^n*x) = 1. - _Paul D. Hanna_, Oct 27 2012
%F E.g.f.: exp(B(x)) where B(x) is the e.g.f. of A003030. - _Andrew Howroyd_, Jan 14 2022
%t a[n_] := a[n] = Module[{A}, A = 1+Sum[a[k]*x^k/k!, {k, 1, n-1}]; n!*SeriesCoefficient[Sum[2^(k^2-k)*x^k/k!/(A /. x -> 2^k*x) , {k, 0, n}], {x, 0, n}]]; a[0]=1; Table[a[n], {n, 0, 13}] (* _Jean-François Alcover_, Dec 15 2014, after _Paul D. Hanna_ *)
%o (PARI) a(n)=local(A=1+sum(k=1,n-1,a(k)*x^k/k!)+x*O(x^n));n!*polcoeff(sum(k=0,n,2^(k^2-k)*x^k/k!/subst(A,x,2^k*x)),n)
%o for(n=0,10,print1(a(n),", ")) \\ _Paul D. Hanna_, Oct 27 2012
%Y The unlabeled version is A350754.
%Y Cf. A003030, A054947, A218393.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 24 2000
%E More terms from _Vladeta Jovovic_, Mar 11 2003
%E Changed offset to 0 and added a(0)=1 by _Paul D. Hanna_, Oct 27 2012
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