%I #20 Jan 04 2021 09:07:09

%S 1,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,1,2,1,0,0,0,0,3,3,1,0,0,0,0,2,9,4,

%T 1,0,0,0,0,1,14,20,6,1,0,0,0,0,1,12,50,40,7,1,0,0,0,0,0,8,82,161,70,9,

%U 1,0,0,0,0,0,5,94,429,433,121,11,1,0,0,0,0,0,2,81,780,1729,1034,189,13,1,0

%N Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) graphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).

%H Hugo Pfoertner, <a href="/A339070/b339070.txt">Table of n, a(n) for n = 1..325</a> (rows 1..25, first 18 rows extracted from Robinson's tables, rows 19-20 from Andrew Howroyd)

%H R. W. Robinson, <a href="http://web.archive.org/web/20041220072855/http://www.cs.uga.edu/~rwr/publications/tables.pdf">Tables of 2-Connected and 3-Connected Graphs by Nodes and Edges</a>, Table IV, pages 4-9.

%F T(n, n) = 1 for n >= 3.

%F T(n, n-1) = A253186(n-3) for n >= 3.

%e Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):

%e 1;

%e 0, 0;

%e 0, 1, 0;

%e 0, 0, 1, 0;

%e 0, 0, 1, 1, 0;

%e 0, 0, 1, 2, 1, 0;

%e 0, 0, 0, 3, 3, 1, 0;

%e 0, 0, 0, 2, 9, 4, 1, 0;

%e 0, 0, 0, 1, 14, 20, 6, 1, 0;

%e 0, 0, 0, 1, 12, 50, 40, 7, 1, 0;

%e 0, 0, 0, 0, 8, 82, 161, 70, 9, 1, 0;

%e 0, 0, 0, 0, 5, 94, 429, 433, 121, 11, 1, 0;

%e ...

%Y Row sums are A010355.

%Y Column sums are A002218.

%Y Cf. A054923, A123534, A253186, A339071 (transpose), A339160.

%K nonn,tabl

%O 1,19

%A _Andrew Howroyd_, Nov 23 2020

%E First row and column removed by _Andrew Howroyd_, Dec 05 2020