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 A359901 #9 Feb 23 2023 21:24:49
%S A359901 1,1,1,1,0,1,2,2,0,1,3,1,0,0,1,4,2,3,0,0,1,6,3,1,0,0,0,1,8,6,2,4,0,0,
%T A359901 0,1,11,7,3,1,0,0,0,0,1,15,10,4,2,5,0,0,0,0,1,20,13,7,3,1,0,0,0,0,0,1,
%U A359901 26,19,11,4,2,6,0,0,0,0,0,1
%N A359901 Triangle read by rows where T(n,k) is the number of integer partitions of n with median k = 1..n.
%C A359901 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%e A359901 Triangle begins:
%e A359901 1
%e A359901 1 1
%e A359901 1 0 1
%e A359901 2 2 0 1
%e A359901 3 1 0 0 1
%e A359901 4 2 3 0 0 1
%e A359901 6 3 1 0 0 0 1
%e A359901 8 6 2 4 0 0 0 1
%e A359901 11 7 3 1 0 0 0 0 1
%e A359901 15 10 4 2 5 0 0 0 0 1
%e A359901 20 13 7 3 1 0 0 0 0 0 1
%e A359901 26 19 11 4 2 6 0 0 0 0 0 1
%e A359901 35 24 14 5 3 1 0 0 0 0 0 0 1
%e A359901 45 34 17 8 4 2 7 0 0 0 0 0 0 1
%e A359901 58 42 23 12 5 3 1 0 0 0 0 0 0 0 1
%e A359901 For example, row n = 9 counts the following partitions:
%e A359901 (7,1,1) (5,2,2) (3,3,3) (4,4,1) . . . . (9)
%e A359901 (6,1,1,1) (6,2,1) (4,3,2)
%e A359901 (3,3,1,1,1) (3,2,2,2) (5,3,1)
%e A359901 (4,2,1,1,1) (4,2,2,1)
%e A359901 (5,1,1,1,1) (4,3,1,1)
%e A359901 (3,2,1,1,1,1) (2,2,2,2,1)
%e A359901 (4,1,1,1,1,1) (3,2,2,1,1)
%e A359901 (2,2,1,1,1,1,1)
%e A359901 (3,1,1,1,1,1,1)
%e A359901 (2,1,1,1,1,1,1,1)
%e A359901 (1,1,1,1,1,1,1,1,1)
%t A359901 Table[Length[Select[IntegerPartitions[n],Median[#]==k&]],{n,15},{k,n}]
%Y A359901 Column k=1 is A027336(n+1).
%Y A359901 For mean instead of median we have A058398, see also A008284, A327482.
%Y A359901 Row sums are A325347.
%Y A359901 The mean statistic is ranked by A326567/A326568.
%Y A359901 Including half-steps gives A359893.
%Y A359901 The odd-length case is A359902.
%Y A359901 The median statistic is ranked by A360005(n)/2.
%Y A359901 First appearances of medians are ranked by A360006, A360007.
%Y A359901 A000041 counts partitions, strict A000009.
%Y A359901 A027193 counts odd-length partitions, strict A067659, ranked by A026424.
%Y A359901 A067538 counts partitions w/ integer mean, strict A102627, ranks A316413.
%Y A359901 A240219 counts partitions w/ the same mean as median, complement A359894.
%Y A359901 Cf. A008289, A237984, A327472, A349156, A359889, A359907.
%K A359901 nonn,tabl
%O A359901 1,7
%A A359901 _Gus Wiseman_, Jan 21 2023