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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
1, 1, 3, 13, 61, 321, 1951, 13693, 109593, 986401, 9864091, 108505101, 1302061333, 16926797473, 236975164791, 3554627472061, 56874039553201, 966858672404673, 17403456103284403, 330665665962403981, 6613313319248079981, 138879579704209680001 (list; graph; refs; listen; history; text; internal format)
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 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}}.

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..n-2.

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

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

E.g.f.: exp(x)*(x^2-x+1)/(1-x). - Alois P. Heinz, Aug 21 2017

PROG

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

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Last modified February 22 16:36 EST 2020. Contains 332140 sequences. (Running on oeis4.)