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

0, 1, 2, 18, 446, 26430, 3596762, 1111506858, 774460794326, 1206342801843750, 4162927142993589122, 31557464707483035620178, 521560130632321900618457246, 18669813048017298278379855511470

Offset: 0

Author

Vladeta Jovovic, Apr 15 2003

Keywords

• nonn

References

• 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.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• Qipeng Kuang, Ondřej Kuželka, Yuanhong Wang, and Yuyi Wang, Bridging Weighted First Order Model Counting and Graph Polynomials, arXiv:2407.11877 [cs.LO], 2024. See p. 33.

Crossrefs

Cf. A003024.

Programs

PARI

\\ here G(n) is A003024 as e.g.f.
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)}
{ concat([0], Vec(serlaplace(log(G(15))))) } \\ Andrew Howroyd, Sep 10 2018

Formula

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

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