This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A134363 #16 Aug 10 2021 11:11:56
%S A134363 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 A134363 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 A134363 -1,0,0,1,0,0,0,0,0,0,0,0,1,3,-2,0,0,2
%N A134363 Irregular triangle read by rows where n-th 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 A134363 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 A134363 Triangle begins:
%e A134363 0;
%e A134363 1;
%e A134363 0, 1;
%e A134363 2;
%e A134363 0, 0, 1;
%e A134363 1, 0;
%e A134363 0, 0, 0, 1;
%e A134363 3;
%e A134363 ...
%e A134363 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 A134363 Cf. A061395, A067255, A134364.
%K A134363 sign,tabf
%O A134363 1,5
%A A134363 _Leroy Quet_, Oct 22 2007