A053598 Number of n-node unlabeled digraphs without isolated nodes.

1, 0, 2, 13, 202, 9390, 1531336, 880492496, 1792477159408, 13026163465206704, 341247403996148180800, 32522568124623933138617088, 11366712907916015518547782806784, 14669074325967499043636521641422216704, 70315641946149306808455637518883828774996992

Offset

0,3

Comments

Equals first differences of A000273.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..60

Formula

O.g.f.: A(x)*(1-x) where A(x) is o.g.f. for A000273. - Geoffrey Critzer, Oct 09 2012

Maple

b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(p[j]-1+add(
      igcd(p[k], p[j]), k=1..j-1)*2, j=1..nops(p)))([l[], 1$n])),
      add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))
    end:
a:= n-> b(n$2, [])-`if`(n=0, 0, b(n-1$2, [])):
seq(a(n), n=0..16);  # Alois P. Heinz, Sep 04 2019

Mathematica

Needs["Combinatorica`"];
nn=15; s=Sum[NumberOfDirectedGraphs[n]x^n, {n, 0, nn}]; CoefficientList[Series[s (1-x), {x, 0, nn}], x]  (* Geoffrey Critzer, Oct 09 2012 *)
Join[{1}, Table[GraphPolynomial[n, x, Directed] /. x -> 1, {n, 0, 15}] // Differences] (* Jean-François Alcover, Feb 04 2015 *)

Crossrefs

Cf. A000273, A002494, A053418 (by # arcs). Row sums of A350908.

Sequence in context: A307066 A361368 A003085 * A193550 A367830 A102585

Adjacent sequences: A053595 A053596 A053597 * A053599 A053600 A053601

Keyword

nonn,nice

Author

Vladeta Jovovic, Apr 10 2000

Status

approved