Search: id:A058128
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%I A058128
%S A058128 1,2,6,28,195,1866,22876,342392,6053445,123456790,2853116706,73686780564,
%T A058128 2103299351335,65751519677858,2234152501943160,81985529216486896,
%U A058128 3231407272993502985,136146740744970718254,6106233505124424657790
%N A058128 a(1)=1, a(n)=(n^n-n)/(n-1)^2 for n >= 2.
%C A058128 Number of acyclic-function digraphs on n vertices. An acyclic-function 
               digraph is a labeled digraph which (i) has no cycles and no loops, 
               (ii) has outdegree 0 or 1 for all vertices and (iii) has x > y when 
               vertex x has outdegree 0 and vertex y has outdegree 1.
%C A058128 This sequence is the sum of antidiagonals of A058127.
%H A058128 T. D. Noe, <a href="b058128.txt">Table of n, a(n) for n=1..100</a>
%H A058128 D. P. Walsh, <a href="http://www.mtsu.edu/~dwalsh/acyclic/acycnote.html">
               Notes on acyclic functions and their directed graphs</a>
%F A058128 a(n) = sum(k=1, n, k*n^(n-k-1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Sep 28 2002
%e A058128 a(3)=6 since the acyclic-function digraphs on 3 vertices are: {(1), (2), 
               (3)} {(1,2), (3)} {(1,3), (2)} {(1,2), (2,3)} {(1,3), (2,3)} {(2,
               1), (1,3)} where (x) denotes a vertex of degree 0 and (x,y) denotes 
               the subgraph consisting of vertices x and y and the arc from x to 
               y.
%Y A058128 Cf. A058127.
%Y A058128 Sequence in context: A084870 A111342 A008964 this_sequence A125812 A093657 
               A006117
%Y A058128 Adjacent sequences: A058125 A058126 A058127 this_sequence A058129 A058130 
               A058131
%K A058128 nice,nonn
%O A058128 1,2
%A A058128 Dennis P. Walsh (dwalsh(AT)mtsu.edu), Nov 14 2000

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