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 A373029 #13 May 20 2024 08:56:59
%S A373029 1,0,1,0,1,1,0,2,1,1,0,2,1,1,1,0,3,1,1,1,1,0,4,2,2,1,1,1,0,5,3,1,2,1,
%T A373029 1,1,0,6,3,1,2,2,1,1,1,0,8,4,3,2,2,2,1,1,1,0,10,5,3,2,3,2,2,1,1,1,0,
%U A373029 12,6,4,2,3,3,2,2,1,1,1,0,15,7,6,3,3,4,3,2,2,1,1,1,0,18,9,6,4,3,4,4,3,2,2,1,1,1
%N A373029 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) is the number of distinct partitions p of n such that max(p) is a multiple of k.
%F A373029 For k > 0, g.f. of column k: Sum_{i>=0} x^(k*i) * Product_{j=1..k*i-1} (1+x^j).
%e A373029 Triangle begins:
%e A373029 1;
%e A373029 0, 1;
%e A373029 0, 1, 1;
%e A373029 0, 2, 1, 1;
%e A373029 0, 2, 1, 1, 1;
%e A373029 0, 3, 1, 1, 1, 1;
%e A373029 0, 4, 2, 2, 1, 1, 1;
%e A373029 0, 5, 3, 1, 2, 1, 1, 1;
%e A373029 0, 6, 3, 1, 2, 2, 1, 1, 1;
%e A373029 0, 8, 4, 3, 2, 2, 2, 1, 1, 1;
%e A373029 0, 10, 5, 3, 2, 3, 2, 2, 1, 1, 1;
%e A373029 0, 12, 6, 4, 2, 3, 3, 2, 2, 1, 1, 1;
%e A373029 0, 15, 7, 6, 3, 3, 4, 3, 2, 2, 1, 1, 1;
%e A373029 0, 18, 9, 6, 4, 3, 4, 4, 3, 2, 2, 1, 1, 1;
%Y A373029 Row sums give A373030.
%Y A373029 Column k=0..3 give A000007, A000009, A026838, A372893.
%Y A373029 T(2n,n) gives A000009.
%Y A373029 Cf. A363048.
%K A373029 nonn,tabl
%O A373029 0,8
%A A373029 _Seiichi Manyama_, May 20 2024