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A243014 Number of acyclic digraphs (DAGS) on n labeled nodes, where the indegree and outdegree of each node is at most 1. 2

%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 3-component graph {A,B,C}, six 2-component graph {{A->B,C},{B->A,C},{A->C,B},{C->A,B},{C->B,A},{B->C,A}}, and six 1-component 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..n-2.

%F a(n) = (n*(a(n-1)+n-2))+1, for n>1, a(1)=1.

%F a(n) = A038154(n)+1.

%F E.g.f.: exp(x)*(x^2-x+1)/(1-x). - _Alois P. Heinz_, Aug 21 2017

%o (MATLAB) @(n)(factorial(n)*sum(1./(factorial(0:n-2)))+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

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Last modified August 18 10:34 EDT 2022. Contains 356212 sequences. (Running on oeis4.)