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A058128
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a(1)=1, a(n)=(n^n-n)/(n-1)^2 for n >= 2.
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7
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1, 2, 6, 28, 195, 1866, 22876, 342392, 6053445, 123456790, 2853116706, 73686780564, 2103299351335, 65751519677858, 2234152501943160, 81985529216486896, 3231407272993502985, 136146740744970718254, 6106233505124424657790
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
This sequence is the sum of antidiagonals of A058127.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
D. P. Walsh, Notes on acyclic functions and their directed graphs
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FORMULA
| a(n) = sum(k=1, n, k*n^(n-k-1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 28 2002
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EXAMPLE
| 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.
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MATHEMATICA
| Join[{1}, Table[(n^n-n)/(n-1)^2, {n, 2, 20}]] (* From Harvey P. Dale, Jul 17 2011 *)
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CROSSREFS
| Cf. A058127.
Sequence in context: A084870 A111342 A008964 * A201959 A178446 A125812
Adjacent sequences: A058125 A058126 A058127 * A058129 A058130 A058131
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KEYWORD
| nice,nonn
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AUTHOR
| Dennis P. Walsh (dwalsh(AT)mtsu.edu), Nov 14 2000
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