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A082402 Number of n-node labeled weakly connected acyclic digraphs. 4


%S 0,1,2,18,446,26430,3596762,1111506858,774460794326,1206342801843750,

%T 4162927142993589122,31557464707483035620178,

%U 521560130632321900618457246,18669813048017298278379855511470

%N Number of n-node labeled weakly connected acyclic digraphs.

%D R. W. Robinson, Counting labeled acyclic digraphs, pp. 263-264 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.

%H Andrew Howroyd, <a href="/A082402/b082402.txt">Table of n, a(n) for n = 0..50</a>

%F E.g.f.: log(B(x)) where B(x) is e.g.f. for A003024.

%F a(n) = A003024(n) - Sum_{k=1..n-1} binomial(n-1, k-1)*a(k)*A003024(n-k).

%o (PARI) \\ here G(n) is A003024 as e.g.f.

%o G(n)={my(v=vector(n+1)); v[1]=1; for(n=1, n, v[n+1]=sum(k=1, n, -(-1)^k*2^(k*(n-k))*v[n-k+1]/k!))/n!; Ser(v)}

%o { concat([0], Vec(serlaplace(log(G(15))))) } \\ _Andrew Howroyd_, Sep 10 2018

%Y Cf. A003024.

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Apr 15 2003

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