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

0,3

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

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