A082403 E.g.f.: 1-1/B(x) where B(x) is e.g.f. for A003024.

0, 1, 1, 13, 373, 24061, 3430021, 1085594413, 765444156373, 1199327541421981, 4150826776751106181, 31511604323119334675053, 521181162682913685911315413, 18663030289006900328937074926621

Offset: 0

Author

Vladeta Jovovic, Apr 15 2003

Keywords

• nonn

References

• R. W. Robinson, Counting labeled acyclic digraphs, p. 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

Crossrefs

Cf. A003024.

Programs

Mathematica

m = 20; b[0] = b[1] = 1;
b[n_] := b[n] = Sum[-(-1)^k Binomial[n, k] 2^(k (n-k)) b[n-k], {k, 1, n}];
B[x_] = Sum[b[n] x^n/n!, {n, 0, m}];
CoefficientList[1 - 1/B[x] + O[x]^(m+1), x] Range[0, m]! (* Jean-François Alcover, Jan 24 2020 *)

PARI

\\ here G(n) gives 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(1-1/G(15)))) } \\ Andrew Howroyd, Sep 10 2018