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A350909 Triangle read by rows: T(n,k) is the number of weakly connected acyclic digraphs on n labeled nodes with k arcs, k=0..n*(n-1).

%I A350909 #7 Jan 29 2022 22:31:28
%S A350909 1,0,2,0,0,12,6,0,0,0,128,186,108,24,0,0,0,0,2000,5640,7840,6540,3330,
%T A350909 960,120,0,0,0,0,0,41472,189480,456720,730830,832370,690300,416160,
%U A350909 178230,51480,9000,720,0,0,0,0,0,0,1075648,7178640,26035800,65339820
%N A350909 Triangle read by rows: T(n,k) is the number of weakly connected acyclic digraphs on n labeled nodes with k arcs, k=0..n*(n-1).
%H A350909 Andrew Howroyd, <a href="/A350909/b350909.txt">Table of n, a(n) for n = 1..1350</a> (rows 1..20)
%e A350909 Triangle begins:
%e A350909   [1] 1;
%e A350909   [2] 0, 2;
%e A350909   [3] 0, 0, 12,   6;
%e A350909   [4] 0, 0,  0, 128,  186,  108,   24;
%e A350909   [5] 0, 0,  0,   0, 2000, 5640, 7840, 6540, 3330, 960, 120;
%e A350909   ...
%o A350909 (PARI)
%o A350909 G(n)={my(v=vector(n+1)); v[1]=1; for(n=1, n, v[n+1]=sum(k=1, n, -(-1)^k*(1+y)^(k*(n-k))*v[n-k+1]/k!))/n!; Ser(v)}
%o A350909 row(n)={Vecrev(n!*polcoef(log(G(n)), n))}
%o A350909 { for(n=1, 6, print(row(n))) }
%Y A350909 Row sums are A082402.
%Y A350909 Leading diagonal is A097629.
%Y A350909 The unlabeled version is A350449.
%Y A350909 Cf. A057273, A062735, A081064.
%K A350909 nonn,tabf
%O A350909 1,3
%A A350909 _Andrew Howroyd_, Jan 29 2022