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A350793 Triangle read by rows: T(n,k) is the number of digraphs on n labeled nodes with k arcs and a global source (or sink), n >= 1, k = 0..(n-1)^2.

%I A350793 #8 Jan 22 2022 23:43:15
%S A350793 1,0,2,0,0,9,12,3,0,0,0,64,252,396,320,144,36,4,0,0,0,0,625,4860,
%T A350793 17060,35900,50775,51300,38340,21540,9075,2800,600,80,5,0,0,0,0,0,
%U A350793 7776,99720,603720,2300310,6206730,12654384,20310840,26385240,28273620,25302960
%N A350793 Triangle read by rows: T(n,k) is the number of digraphs on n labeled nodes with k arcs and a global source (or sink), n >= 1, k = 0..(n-1)^2.
%H A350793 Andrew Howroyd, <a href="/A350793/b350793.txt">Table of n, a(n) for n = 1..2490</a> (rows 1..20)
%e A350793 Triangle begins:
%e A350793   [1] 1;
%e A350793   [2] 0, 2;
%e A350793   [3] 0, 0, 9, 12, 3;
%e A350793   [4] 0, 0, 0, 64, 252, 396, 320, 144, 36, 4;
%e A350793   ...
%o A350793 (PARI)
%o A350793 InitiallyV(n, e=2)={my(v=vector(n)); for(n=1, n, v[n] = n*e^((n-1)^2) - sum(k=1, n-1, binomial(n,k)*e^((n-2)*(n-k))*v[k])); v}
%o A350793 row(n)={Vecrev(InitiallyV(n, 1+'y)[n])}
%o A350793 { for(n=1, 5, print(row(n))) }
%Y A350793 Row sums are A350792.
%Y A350793 The leading diagonal is A000169.
%Y A350793 The unlabeled version is A350797.
%Y A350793 Cf. A057274, A350791.
%K A350793 nonn,tabf
%O A350793 1,3
%A A350793 _Andrew Howroyd_, Jan 17 2022