A082402 - OEIS

A082402

Number of n-node labeled weakly connected acyclic digraphs.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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.

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).

PROG

(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

CROSSREFS

Cf. A003024.

Sequence in context: A260656 A141074 A351052 * A208055 A306655 A156907

Adjacent sequences: A082399 A082400 A082401 * A082403 A082404 A082405

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Apr 15 2003

STATUS

approved