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Number of acyclic n-multidigraphs on n labeled vertices.
2

%I #11 Jun 14 2022 08:21:38

%S 1,1,5,289,267249,5004309601,2306766500044453,30888553723078503825409,

%T 13859983478324955468951984020417,

%U 236220504431931018509832208799998200000001,170953602414073201827802109472335543681457702850676901

%N Number of acyclic n-multidigraphs on n labeled vertices.

%H Seiichi Manyama, <a href="/A354962/b354962.txt">Table of n, a(n) for n = 0..35</a>

%o (Ruby)

%o def ncr(n, r)

%o return 1 if r == 0

%o (n - r + 1..n).inject(:*) / (1..r).inject(:*)

%o end

%o def A(k, n)

%o ary = [1]

%o (1..n).each{|i| ary << (1..i).inject(0){|s, j| s + (-1) ** (j + 1) * (k + 1) ** (j * (i - j)) * ncr(i, j) * ary[-j]}}

%o ary[-1]

%o end

%o def A354962(n)

%o (0..n).map{|i| A(i, i)}

%o end

%o p A354962(10)

%Y Main diagonal of A339768.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 13 2022