cp's OEIS Frontend

A350789 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected digraphs with n arcs and k vertices, k = 1..n+1.

%I A350789 #10 Jan 29 2022 22:31:06
%S A350789 1,0,1,0,1,3,0,0,4,8,0,0,4,22,27,0,0,1,37,108,91,0,0,1,47,326,582,350,
%T A350789 0,0,0,38,667,2432,3024,1376,0,0,0,27,1127,7694,17314,16008,5743,0,0,
%U A350789 0,13,1477,19646,74676,117312,84494,24635
%N A350789 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected digraphs with n arcs and k vertices, k = 1..n+1.
%H A350789 Andrew Howroyd, <a href="/A350789/b350789.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%e A350789 Triangle begins:
%e A350789   1;
%e A350789   0, 1;
%e A350789   0, 1, 3;
%e A350789   0, 0, 4,  8;
%e A350789   0, 0, 4, 22,   27;
%e A350789   0, 0, 1, 37,  108,   91;
%e A350789   0, 0, 1, 47,  326,  582,   350;
%e A350789   0, 0, 0, 38,  667, 2432,  3024,  1376;
%e A350789   0, 0, 0, 27, 1127, 7694, 17314, 16008, 5743;
%e A350789   ...
%o A350789 (PARI) \\ See A054733 for G, InvEulerMTS
%o A350789 T(n)={my(p=InvEulerMTS(sum(i=0, n, G(i, y+O(y^n))*x^i, O(x*x^n)))); vector(n, n, Vec(O(x^n)+polcoef(p,n-1,y)/x, -n))}
%o A350789 { my(A=T(10)); for(n=1, #A, print(A[n])) }
%Y A350789 Row sums are A053454.
%Y A350789 Column sums are A003085.
%Y A350789 Main diagonal is A000238.
%Y A350789 Cf. A054733 (transpose), A350450 (acyclic), A350753 (strongly connected).
%K A350789 nonn,tabl
%O A350789 0,6
%A A350789 _Andrew Howroyd_, Jan 28 2022