%I
%S 0,1,0,1,2,0,0,1,1,0,0,0,0,1,3,0,2,1,1,1,0,0,0,0,1,2,1,0,0,0,0,0,1,
%T 1,1,0,1,0,1,0,4,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,1,2,2,1,0,1,1,1,1,
%U 1,0,0,1,0,0,0,0,0,0,0,0,1,3,2,0,0,2
%N Irregular triangle read by rows where nth row (of A061395(n) terms, for n>=2) is such that n = Product_{j=1..A061395(n)} prime(j)^(Sum_{k=1..j} T(n,k)). Row 1 is {0}.
%C The rows of this triangle also give all the ordered ways that a finite number of integers can be arranged so that their partial sums, from left to right, are all nonnegative and their total sum is positive.
%e Triangle begins:
%e 0;
%e 1;
%e 0, 1;
%e 2;
%e 0, 0, 1;
%e 1, 0;
%e 0, 0, 0, 1;
%e 3;
%e ...
%e Row 20 is {2, 2, 1}. So 20 = prime(1)^T(20,1) * prime(2)^(T(20,1) + T(20,2)) * prime(3)^(T(20,1) + T(20,2) + T(20,3)) = 2^2 * 3^(2  2) * 5^(2  2 + 1) = 2^2 * 3^0 * 5^1.
%Y Cf. A061395, A067255, A134364.
%K sign,tabf
%O 1,5
%A _Leroy Quet_, Oct 22 2007
