%I #13 Aug 05 2014 14:13:44

%S 0,1,1,1,1,2,2,1,1,2,3,5,4,2,1,1,2,4,8,13,15,16,11,5,2,1,1,2,4,9,19,

%T 35,55,75,83,72,51,29,13,5,2,1,1,2,4,10,22,50,105,196,338,511,649,695,

%U 627,473,304,172,83,35,14,5,2,1

%N T(n,k) is the number of unlabeled graphs of n vertices and k edges that have endpoints, where an endpoint is a vertex with degree 1.

%C The length of the rows are 1,1,2,4,7,11,16,22,...: (n-1)*(n-2)/2 + 1 = A152947(n).

%C T(n,k) = 0 if k > (n-1)*(n-2)/2 + 1. (Cf. A245796)

%e First few rows of irregular triangle are:

%e ..0

%e ..1

%e ..1....1

%e ..1....2....2....1

%e ..1....2....3....5....4....2....1

%e ..1....2....4....8...13...15...16...11....5....2....1

%e ..1....2....4....9...19...35...55...75...83...72...51...29...13....5....2....1

%e ...

%Y Cf. A245796. Sum of n-th row is equal to A141580(n).

%K nonn,tabf

%O 1,6

%A _Chai Wah Wu_, Aug 02 2014