This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A243014 #38 Feb 16 2025 08:33:22
%S A243014 1,1,3,13,61,321,1951,13693,109593,986401,9864091,108505101,
%T A243014 1302061333,16926797473,236975164791,3554627472061,56874039553201,
%U A243014 966858672404673,17403456103284403,330665665962403981,6613313319248079981,138879579704209680001
%N A243014 Number of acyclic digraphs (DAGS) on n labeled nodes, where the indegree and outdegree of each node is at most 1.
%C A243014 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 A243014 Alois P. Heinz, <a href="/A243014/b243014.txt">Table of n, a(n) for n = 0..449</a>
%H A243014 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AcyclicDigraph.html">Acyclic Digraph.</a>
%H A243014 <a href="/index/Di#digraphs">Index entries for sequences related to digraphs (or directed graphs)</a>
%F A243014 a(n) = (n!*Sum(1/k!))+1, k=0..n-2.
%F A243014 a(n) = (n*(a(n-1)+n-2))+1, for n>1, a(1)=1.
%F A243014 a(n) = A038154(n)+1.
%F A243014 E.g.f.: exp(x)*(x^2-x+1)/(1-x). - _Alois P. Heinz_, Aug 21 2017
%o A243014 (MATLAB) @(n)(factorial(n)*sum(1./(factorial(0:n-2)))+1)
%Y A243014 Cf. A003024, A038154.
%K A243014 nonn
%O A243014 0,3
%A A243014 _Shuaib Ahmed S_, May 29 2014
%E A243014 a(0)=1 prepended, one term corrected, more terms added by _Alois P. Heinz_, Aug 21 2017