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 A271584 #10 Apr 10 2016 23:23:50
%S A271584 0,0,0,0,0,1,0,0,2,0,1,4,0,0,2,6,0,1,4,9,0,0,2,6,12,0,1,4,9,16,0,0,2,
%T A271584 6,12,20,0,1,4,9,16,25,0,0,2,6,12,20,30,0,1,4,9,16,25,36,0,0,2,6,12,
%U A271584 20,30,42,0,1,4,9,16,25,36,49
%N A271584 Irregular triangle read by rows: alternate (k-1)*k, k^2, for k = 0 to n.
%C A271584 This is the irregular triangle e(n) mentioned in A269837.
%C A271584 Last number: 0, 0, 0, 1, 2, 4, 6, 9, 12, 16, 20, 25, ... = A002620 with a third initial 0.
%C A271584 Row sums: 0, 0, 0, 1, 2, 5, 8, 14, 20, 30, 40, ... = A006918 with three initial 0.
%C A271584 Columns: the sum of the first two terms is A000384(n).
%e A271584 Irregular triangle:
%e A271584 0,
%e A271584 0,
%e A271584 0, 0,
%e A271584 0, 1,
%e A271584 0, 0, 2,
%e A271584 0, 1, 4,
%e A271584 0, 0, 2, 6,
%e A271584 0, 1, 4, 9,
%e A271584 0, 0, 2, 6, 12,
%e A271584 0, 1, 4, 9, 16,
%e A271584 0, 0, 2, 6, 12, 20,
%e A271584 0, 1, 4, 9, 16, 25,
%e A271584 etc.
%t A271584 Flatten[Transpose /@ Table[{k (k - 1), k^2}, {n, 0, 7}, {k, 0, n}]] (* _Michael De Vlieger_, Apr 10 2016 *)
%Y A271584 Cf. A000290, A000384, A002262, A006918, A161680, A269837.
%K A271584 nonn,tabf
%O A271584 0,9
%A A271584 _Paul Curtz_, Apr 10 2016