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A354962 Number of acyclic n-multidigraphs on n labeled vertices.

%I A354962 #11 Jun 14 2022 08:21:38
%S A354962 1,1,5,289,267249,5004309601,2306766500044453,30888553723078503825409,
%T A354962 13859983478324955468951984020417,
%U A354962 236220504431931018509832208799998200000001,170953602414073201827802109472335543681457702850676901
%N A354962 Number of acyclic n-multidigraphs on n labeled vertices.
%H A354962 Seiichi Manyama, <a href="/A354962/b354962.txt">Table of n, a(n) for n = 0..35</a>
%o A354962 (Ruby)
%o A354962 def ncr(n, r)
%o A354962   return 1 if r == 0
%o A354962   (n - r + 1..n).inject(:*) / (1..r).inject(:*)
%o A354962 end
%o A354962 def A(k, n)
%o A354962   ary = [1]
%o A354962   (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 A354962   ary[-1]
%o A354962 end
%o A354962 def A354962(n)
%o A354962   (0..n).map{|i| A(i, i)}
%o A354962 end
%o A354962 p A354962(10)
%Y A354962 Main diagonal of A339768.
%K A354962 nonn
%O A354962 0,3
%A A354962 _Seiichi Manyama_, Jun 13 2022