%I
%S 1,1,3,13,61,321,1951,13693,109593,986401,9864091,108505101,
%T 1302061333,16926797473,236975164791,3554627472061,56874039553201,
%U 966858672404673,17403456103284403,330665665962403981,6613313319248079981,138879579704209680001
%N Number of acyclic digraphs (DAGS) on n labeled nodes, where the indegree and outdegree of each node is at most 1.
%C a(n) is the number of acyclic digraphs (DAGS) on n labeled nodes, where the indegree and outdegree of each node is at most 1. For example, with vertex set {A,B,C} the possible ways are: one 3component graph {A,B,C}, six 2component graph {{A>B,C},{B>A,C},{A>C,B},{C>A,B},{C>B,A},{B>C,A}}, and six 1component graph {{A>B>C},{B>A>C},{A>C>B},{C>A>B},{C>B>A},{B>C>A}}.
%H Alois P. Heinz, <a href="/A243014/b243014.txt">Table of n, a(n) for n = 0..449</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AcyclicDigraph.html">Acyclic Digraph.</a>
%H <a href="/index/Di#digraphs">Index entries for sequences related to digraphs (or directed graphs)</a>
%F a(n) = (n!*Sum(1/k!))+1, k=0..n2.
%F a(n) = (n*(a(n1)+n2))+1, for n>1, a(1)=1.
%F a(n) = A038154(n)+1.
%F E.g.f.: exp(x)*(x^2x+1)/(1x).  _Alois P. Heinz_, Aug 21 2017
%o (MATLAB) @(n)(factorial(n)*sum(1./(factorial(0:n2)))+1)
%Y Cf. A003024, A038154.
%K nonn
%O 0,3
%A _Shuaib Ahmed S_, May 29 2014
%E a(0)=1 prepended, one term corrected, more terms added by _Alois P. Heinz_, Aug 21 2017
