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 A325200 #16 Jan 13 2024 13:08:45
%S A325200 1,1,0,0,2,0,1,0,2,0,0,3,0,2,0,0,3,2,0,2,0,1,0,6,2,0,2,0,0,4,3,4,2,0,
%T A325200 2,0,0,6,2,6,4,2,0,2,0,0,4,9,5,4,4,2,0,2,0,1,0,15,6,8,4,4,2,0,2,0,0,5,
%U A325200 12,12,9,6,4,4,2,0,2,0,0,10,6,21,10,12,6,4,4,2,0,2,0
%N A325200 Regular triangle read by rows where T(n,k) is the number of integer partitions of n such that the difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram is k.
%H A325200 Andrew Howroyd, <a href="/A325200/b325200.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%H A325200 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000380">St000380: Half the perimeter of the largest rectangle that fits inside the diagram of an integer partition</a>
%H A325200 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000384">St000384: The maximal part of the shifted composition of an integer partition</a>
%H A325200 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000783">St000783: The maximal number of occurrences of a colour in a proper colouring of a Ferrers diagram</a>
%F A325200 Sum_{k=1..n} k*T(n,k) = A366157(n) - A368986(n). - _Andrew Howroyd_, Jan 13 2024
%e A325200 Triangle begins:
%e A325200 1
%e A325200 1 0
%e A325200 0 2 0
%e A325200 1 0 2 0
%e A325200 0 3 0 2 0
%e A325200 0 3 2 0 2 0
%e A325200 1 0 6 2 0 2 0
%e A325200 0 4 3 4 2 0 2 0
%e A325200 0 6 2 6 4 2 0 2 0
%e A325200 0 4 9 5 4 4 2 0 2 0
%e A325200 1 0 15 6 8 4 4 2 0 2 0
%e A325200 0 5 12 12 9 6 4 4 2 0 2 0
%e A325200 0 10 6 21 10 12 6 4 4 2 0 2 0
%e A325200 0 10 12 20 18 13 10 6 4 4 2 0 2 0
%e A325200 0 5 27 20 23 16 16 10 6 4 4 2 0 2 0
%e A325200 1 0 38 22 32 22 19 14 10 6 4 4 2 0 2 0
%e A325200 0 6 34 38 34 35 20 22 14 10 6 4 4 2 0 2 0
%e A325200 0 15 22 57 44 40 34 23 20 14 10 6 4 4 2 0 2 0
%e A325200 0 20 20 71 55 54 45 32 26 20 14 10 6 4 4 2 0 2 0
%e A325200 0 15 43 70 71 66 60 44 35 24 20 14 10 6 4 4 2 0 2 0
%e A325200 0 6 74 64 99 83 70 65 42 38 24 20 14 10 6 4 4 2 0 2 0
%e A325200 Row n = 9 counts the following partitions (empty columns not shown):
%e A325200 (432) (333) (54) (63) (72) (81) (9)
%e A325200 (3321) (441) (621) (6111) (711) (21111111) (111111111)
%e A325200 (4221) (522) (22221) (222111) (2211111)
%e A325200 (4311) (531) (51111) (411111) (3111111)
%e A325200 (3222) (321111)
%e A325200 (5211)
%e A325200 (32211)
%e A325200 (33111)
%e A325200 (42111)
%t A325200 otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325200 otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325200 Table[Length[Select[IntegerPartitions[n],otbmax[#]-otb[#]==k&]],{n,0,20},{k,0,n}]
%o A325200 (PARI) row(n)={my(r=vector(n+1)); forpart(p=n, my(b=#p,c=0); for(i=1, #p, my(x=#p-i+p[i]); b=min(b,x); c=max(c,x)); r[c-b+1]++); r} \\ _Andrew Howroyd_, Jan 12 2024
%Y A325200 Row sums are A000041. Column k = 1 is A325191. Column k = 2 is A325199.
%Y A325200 T(n,k) = A325189(n,k) - A325188(n,k).
%Y A325200 Cf. A046660, A065770, A071724, A243055, A325169, A325178, A325195, A325196, A325197, A366157, A368986.
%K A325200 nonn,tabl
%O A325200 0,5
%A A325200 _Gus Wiseman_, Apr 11 2019