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

0,4

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

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 *)

Prog

(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

Crossrefs

Cf. A003024.

Sequence in context: A009040 A009085 A012013 * A171656 A320458 A320635

Adjacent sequences: A082400 A082401 A082402 * A082404 A082405 A082406

Keyword

nonn

Author

Vladeta Jovovic, Apr 15 2003

Status

approved