|
%I #23 Nov 20 2023 04:21:54
%S 1,0,2,13,202,9390,1531336,880492496,1792477159408,13026163465206704,
%T 341247403996148180800,32522568124623933138617088,
%U 11366712907916015518547782806784,14669074325967499043636521641422216704,70315641946149306808455637518883828774996992
%N Number of n-node unlabeled digraphs without isolated nodes.
%C Equals first differences of A000273.
%H Alois P. Heinz, <a href="/A053598/b053598.txt">Table of n, a(n) for n = 0..60</a>
%F O.g.f.: A(x)*(1-x) where A(x) is o.g.f. for A000273. - _Geoffrey Critzer_, Oct 09 2012
%p b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(p[j]-1+add(
%p igcd(p[k], p[j]), k=1..j-1)*2, j=1..nops(p)))([l[], 1$n])),
%p add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i))
%p end:
%p a:= n-> b(n$2, [])-`if`(n=0, 0, b(n-1$2, [])):
%p seq(a(n), n=0..16); # _Alois P. Heinz_, Sep 04 2019
%t Needs["Combinatorica`"];
%t 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 *)
%t Join[{1}, Table[GraphPolynomial[n, x, Directed] /. x -> 1, {n, 0, 15}] // Differences] (* _Jean-François Alcover_, Feb 04 2015 *)
%Y Cf. A000273, A002494, A053418 (by # arcs). Row sums of A350908.
%K nonn,nice
%O 0,3
%A _Vladeta Jovovic_, Apr 10 2000
|
