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A350914 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected oriented graphs with n arcs and k vertices, k = 1..n+1.

%I A350914 #9 Jan 29 2022 22:31:33
%S A350914 1,0,1,0,0,3,0,0,2,8,0,0,0,12,27,0,0,0,10,68,91,0,0,0,4,127,395,350,0,
%T A350914 0,0,0,144,1144,2170,1376,0,0,0,0,107,2393,9139,11934,5743,0,0,0,0,50,
%U A350914 3767,28606,67104,64892,24635,0,0,0,0,12,4500,71583,288331,468702,352286,108968
%N A350914 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected oriented graphs with n arcs and k vertices, k = 1..n+1.
%H A350914 Andrew Howroyd, <a href="/A350914/b350914.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%e A350914 Triangle begins:
%e A350914   1;
%e A350914   0, 1;
%e A350914   0, 0, 3;
%e A350914   0, 0, 2,  8;
%e A350914   0, 0, 0, 12,  27;
%e A350914   0, 0, 0, 10,  68,   91;
%e A350914   0, 0, 0,  4, 127,  395,  350;
%e A350914   0, 0, 0,  0, 144, 1144, 2170, 1376;
%e A350914   ...
%o A350914 (PARI) \\ See A350734 for G, InvEulerMTS.
%o A350914 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 A350914 { my(A=T(10)); for(n=1, #A, print(A[n])) }
%Y A350914 Row sums are A350915.
%Y A350914 Column sums are A086345.
%Y A350914 Cf. A350734 (transpose), A350789 (digraphs).
%K A350914 nonn,tabl
%O A350914 0,6
%A A350914 _Andrew Howroyd_, Jan 29 2022