cp's OEIS Frontend

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

%I A082402 #15 Jul 25 2024 10:47:53
%S A082402 0,1,2,18,446,26430,3596762,1111506858,774460794326,1206342801843750,
%T A082402 4162927142993589122,31557464707483035620178,
%U A082402 521560130632321900618457246,18669813048017298278379855511470
%N A082402 Number of n-node labeled weakly connected acyclic digraphs.
%D A082402 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 A082402 Andrew Howroyd, <a href="/A082402/b082402.txt">Table of n, a(n) for n = 0..50</a>
%H A082402 Qipeng Kuang, Ondřej Kuželka, Yuanhong Wang, and Yuyi Wang, <a href="https://arxiv.org/abs/2407.11877">Bridging Weighted First Order Model Counting and Graph Polynomials</a>, arXiv:2407.11877 [cs.LO], 2024. See p. 33.
%F A082402 E.g.f.: log(B(x)) where B(x) is e.g.f. for A003024.
%F A082402 a(n) = A003024(n) - Sum_{k=1..n-1} binomial(n-1, k-1)*a(k)*A003024(n-k).
%o A082402 (PARI) \\ here G(n) is A003024 as e.g.f.
%o A082402 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 A082402 { concat([0], Vec(serlaplace(log(G(15))))) } \\ _Andrew Howroyd_, Sep 10 2018
%Y A082402 Cf. A003024.
%K A082402 nonn
%O A082402 0,3
%A A082402 _Vladeta Jovovic_, Apr 15 2003