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 A168020 #19 Jan 13 2023 16:26:51
%S A168020 1,2,0,3,1,0,5,0,0,0,7,2,1,0,0,11,0,0,0,0,0,15,3,0,1,0,0,0,22,0,2,0,0,
%T A168020 0,0,0,30,5,0,0,1,0,0,0,0,42,0,0,0,0,0,0,0,0,0,56,7,3,2,0,1,0,0,0,0,0,
%U A168020 77,0,0,0,0,0,0,0,0,0,0,0,101,11,0,0,0,0,1,0,0,0,0,0,0
%N A168020 Square array read by antidiagonals in which row n lists the number of partitions of n into parts divisible by k.
%C A168020 In the square array, note that the column k starts with k-1 zeros. Then list each partition number of positive integers followed by k-1 zeros. See A000041, which is the main entry for this sequence.
%H A168020 G. C. Greubel, <a href="/A168020/b168020.txt">Antidiagonals n = 1..50, flattened</a>
%H A168020 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpatru.jpg">Illustration of the shell model of partitions (2D and 3D)</a>
%H A168020 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa2dt.jpg">Illustration of the shell model of partitions (2D view)</a>
%H A168020 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpa3dt.jpg">Illustration of the shell model of partitions (3D view)</a>
%F A168020 A(n, k) = A000041(n/k) if k divides n, otherwise A(n, k) = 0 (array).
%F A168020 A(n, 1) = A(n*k, k) = A000041(n).
%F A168020 From _G. C. Greubel_, Jan 12 2023: (Start)
%F A168020 T(n, k) = A000041((n-k+1)/k) if k divides (n-k+1), otherwise T(n, k) = 0 (triangle).
%F A168020 T(n, 1) = A000041(n).
%F A168020 T(2*n, n) = 2*A000007(n-1), n >= 1. (End)
%e A168020 The array, A(n, k), begins:
%e A168020 n | k = 1 2 3 4 5 6 7 8 9 10 11 12
%e A168020 ---+--------------------------------------------------
%e A168020 1 | 1 0 0 0 0 0 0 0 0 0 0 0
%e A168020 2 | 2 1 0 0 0 0 0 0 0 0 0 0
%e A168020 3 | 3 0 1 0 0 0 0 0 0 0 0 0
%e A168020 4 | 5 2 0 1 0 0 0 0 0 0 0 0
%e A168020 5 | 7 0 0 0 1 0 0 0 0 0 0 0
%e A168020 6 | 11 3 2 0 0 1 0 0 0 0 0 0
%e A168020 7 | 15 0 0 0 0 0 1 0 0 0 0 0
%e A168020 8 | 22 5 0 2 0 0 0 1 0 0 0 0
%e A168020 9 | 30 0 3 0 0 0 0 0 1 0 0 0
%e A168020 10 | 42 7 0 0 2 0 0 0 0 1 0 0
%e A168020 11 | 56 0 0 0 0 0 0 0 0 0 1 0
%e A168020 12 | 77 11 5 3 0 2 0 0 0 0 0 1
%e A168020 ...
%e A168020 Antidiagonal triangle, T(n,k), begins as:
%e A168020 1;
%e A168020 2, 0;
%e A168020 3, 1, 0;
%e A168020 5, 0, 0, 0;
%e A168020 7, 2, 1, 0, 0;
%e A168020 11, 0, 0, 0, 0, 0;
%e A168020 15, 3, 0, 1, 0, 0, 0;
%e A168020 22, 0, 2, 0, 0, 0, 0, 0;
%e A168020 30, 5, 0, 0, 1, 0, 0, 0, 0;
%e A168020 42, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%t A168020 T[n_, k_]:= If[IntegerQ[(n-k+1)/k], PartitionsP[(n-k+1)/k], 0];
%t A168020 Table[T[n, k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Jan 12 2023 *)
%o A168020 (SageMath)
%o A168020 def A168020(n,k): return number_of_partitions((n-k+1)/k) if ((n-k+1)%k)==0 else 0
%o A168020 flatten([[A168020(n,k) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Jan 12 2023
%Y A168020 Cf. A000007, A000041, A035377, A035444, A135010, A138121.
%Y A168020 Cf. A168016, A168017, A168018, A168019, A168021. [From _Omar E. Pol_, Nov 23 2009]
%K A168020 easy,nonn,tabl
%O A168020 1,2
%A A168020 _Omar E. Pol_, Nov 20 2009
%E A168020 Edited by _Omar E. Pol_, Nov 21 2009
%E A168020 Edited by _Charles R Greathouse IV_, Mar 23 2010
%E A168020 Edited by _Max Alekseyev_, May 07 2010