

A243014


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


2



1, 1, 3, 13, 61, 321, 1951, 13693, 109593, 986401, 9864091, 108505101, 1302061333, 16926797473, 236975164791, 3554627472061, 56874039553201, 966858672404673, 17403456103284403, 330665665962403981, 6613313319248079981, 138879579704209680001
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OFFSET

0,3


COMMENTS

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}}.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..449
Eric Weisstein's World of Mathematics, Acyclic Digraph.
Index entries for sequences related to digraphs (or directed graphs)


FORMULA

a(n) = (n!*Sum(1/k!))+1, k=0..n2.
a(n) = (n*(a(n1)+n2))+1, for n>1, a(1)=1.
a(n) = A038154(n)+1.
E.g.f.: exp(x)*(x^2x+1)/(1x).  Alois P. Heinz, Aug 21 2017


PROG

(MATLAB) @(n)(factorial(n)*sum(1./(factorial(0:n2)))+1)


CROSSREFS

Cf. A003024, A038154.
Sequence in context: A256333 A200215 A074548 * A258799 A246689 A141786
Adjacent sequences: A243011 A243012 A243013 * A243015 A243016 A243017


KEYWORD

nonn


AUTHOR

Shuaib Ahmed S, May 29 2014


EXTENSIONS

a(0)=1 prepended, one term corrected, more terms added by Alois P. Heinz, Aug 21 2017


STATUS

approved



