A058128 a(1) = 1, a(n) = (n^n-n)/(n-1)^2 for n >= 2.

1, 2, 6, 28, 195, 1866, 22876, 342392, 6053445, 123456790, 2853116706, 73686780564, 2103299351335, 65751519677858, 2234152501943160, 81985529216486896, 3231407272993502985, 136146740744970718254, 6106233505124424657790, 290464265927977839335180

Offset: 1

Author

Dennis P. Walsh, Nov 14 2000

Keywords

• nice
• nonn

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.

Conjecture: For even n, a(n) is prime or a weak Fermat pseudoprime to base n. - Davide Rotondo, Nov 06 2024

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..100
• D. P. Walsh, Notes on acyclic functions and their directed graphs

Crossrefs

Cf. A058127.

Programs

Mathematica

Join[{1},Table[(n^n-n)/(n-1)^2,{n,2,20}]] (* Harvey P. Dale, Jul 17 2011 *)

Formula

a(n) = Sum_{k=1..n} k*n^(n-k-1). - Benoit Cloitre, Sep 28 2002