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%I #17 Aug 25 2021 10:22:50
%S 1,2,6,28,195,1866,22876,342392,6053445,123456790,2853116706,
%T 73686780564,2103299351335,65751519677858,2234152501943160,
%U 81985529216486896,3231407272993502985,136146740744970718254,6106233505124424657790,290464265927977839335180
%N a(1) = 1, a(n) = (n^n-n)/(n-1)^2 for n >= 2.
%C 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 This sequence is the sum of antidiagonals of A058127.
%H T. D. Noe, <a href="/A058128/b058128.txt">Table of n, a(n) for n=1..100</a>
%H D. P. Walsh, <a href="http://www.mtsu.edu/~dwalsh/acyclic/acycnote.html">Notes on acyclic functions and their directed graphs</a>
%F a(n) = Sum_{k=1..n} k*n^(n-k-1). - _Benoit Cloitre_, Sep 28 2002
%e 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.
%t Join[{1},Table[(n^n-n)/(n-1)^2,{n,2,20}]] (* _Harvey P. Dale_, Jul 17 2011 *)
%Y Cf. A058127.
%K nice,nonn
%O 1,2
%A _Dennis P. Walsh_, Nov 14 2000
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