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 A362208 #14 Apr 16 2023 20:37:29
%S A362208 1,0,0,2,0,2,0,4,0,2,6,0,2,6,0,0,12,0,0,18,0,0,24,24,0,0,30,24,0,0,42,
%T A362208 48,0,0,42,72,0,0,48,120,0,0,48,144,120,0,0,48,216,120,0,0,42,264,240,
%U A362208 0,0,42,360,360,0,0,30,432,600,0,0,24,552,840,0,0,18,648,1200,720
%N A362208 Irregular triangle read by rows: T(n, k) is the number of compositions (ordered partitions) of n into exactly k distinct parts between the members of [k^2].
%e A362208 The irregular triangle begins:
%e A362208 1;
%e A362208 0;
%e A362208 0, 2;
%e A362208 0, 2;
%e A362208 0, 4;
%e A362208 0, 2, 6;
%e A362208 0, 2, 6;
%e A362208 0, 0, 12;
%e A362208 0, 0, 18;
%e A362208 0, 0, 24, 24;
%e A362208 0, 0, 30, 24;
%e A362208 0, 0, 42, 48;
%e A362208 0, 0, 42, 72;
%e A362208 0, 0, 48, 120;
%e A362208 0, 0, 48, 144, 120;
%e A362208 ...
%e A362208 T(7,3) = 6 since we have: 1+2+4, 1+4+2, 2+1+4, 2+4+1, 4+1+2, 4+2+1.
%t A362208 Flatten[Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n,All,Range[k^2]], UnsameQ@@#&], Length[#]==k&]], {n, 21}, {k, Floor[(Sqrt[8n+1]-1)/2]}]] (* After _Gus Wiseman_ in A072574 *)
%Y A362208 Cf. A000290, A003056 (row lengths), A072574, A216652.
%Y A362208 Cf. A362209, A362221 (unordered partitions).
%K A362208 nonn,tabf
%O A362208 1,4
%A A362208 _Stefano Spezia_, Apr 11 2023