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 A124944 #18 Jul 13 2023 16:28:48
%S A124944 1,1,1,1,1,1,2,1,1,1,3,1,1,1,1,4,3,1,1,1,1,6,4,1,1,1,1,1,8,6,3,1,1,1,
%T A124944 1,1,11,8,5,1,1,1,1,1,1,15,11,7,3,1,1,1,1,1,1,20,15,9,5,1,1,1,1,1,1,1,
%U A124944 26,21,12,8,3,1,1,1,1,1,1,1,35,27,16,10,5,1,1,1,1,1,1,1,1,45,37,21,13,8,3
%N A124944 Table, number of partitions of n with k as high median.
%C A124944 For a multiset with an odd number of elements, the high median is the same as the median. For a multiset with an even number of elements, the high median is the larger of the two central elements.
%C A124944 This table may be read as an upper right triangle with n >= 1 as column index and k >= 1 as row index. - _Peter Munn_, Jul 16 2017
%C A124944 Arrange the parts of a partition nonincreasing order. Remove the last part, then the first, then the last remaining part, then the first remaining part, and continue until only a single number, the high median, remains. - _Clark Kimberling_, May 14 2019
%e A124944 For the partition [2,1^2], the sole middle element is 1, so that is the high median. For [3,2,1^2], the two middle elements are 1 and 2; the high median is the larger, 2.
%e A124944 From _Gus Wiseman_, Jul 12 2023: (Start)
%e A124944 Triangle begins:
%e A124944 1
%e A124944 1 1
%e A124944 1 1 1
%e A124944 2 1 1 1
%e A124944 3 1 1 1 1
%e A124944 4 3 1 1 1 1
%e A124944 6 4 1 1 1 1 1
%e A124944 8 6 3 1 1 1 1 1
%e A124944 11 8 5 1 1 1 1 1 1
%e A124944 15 11 7 3 1 1 1 1 1 1
%e A124944 20 15 9 5 1 1 1 1 1 1 1
%e A124944 26 21 12 8 3 1 1 1 1 1 1 1
%e A124944 35 27 16 10 5 1 1 1 1 1 1 1 1
%e A124944 45 37 21 13 8 3 1 1 1 1 1 1 1 1
%e A124944 58 48 29 16 11 5 1 1 1 1 1 1 1 1 1
%e A124944 Row n = 8 counts the following partitions:
%e A124944 (611) (521) (431) (44) (53) (62) (71) (8)
%e A124944 (5111) (422) (332)
%e A124944 (41111) (4211) (3311)
%e A124944 (32111) (3221)
%e A124944 (311111) (2222)
%e A124944 (221111) (22211)
%e A124944 (2111111)
%e A124944 (11111111)
%e A124944 (End)
%t A124944 Map[BinCounts[#, {1, #[[1]] + 1, 1}] &[Map[#[[Floor[(Length[#] + 1)/2]]] &, IntegerPartitions[#]]] &, Range[13]] (* _Peter J. C. Moses_, May 14 2019 *)
%Y A124944 Row sums are A000041.
%Y A124944 Column k = 1 is A027336(n-1), ranks A364056.
%Y A124944 Column k = 1 in the low version is A027336, ranks A363488.
%Y A124944 The low version of this triangle is A124943.
%Y A124944 The rank statistic for this triangle is A363942, low version A363941.
%Y A124944 A version for mean instead of median is A363946, low A363945.
%Y A124944 A version for mode instead of median is A363953, low A363952.
%Y A124944 A008284 counts partitions by length, maximum, or decreasing mean.
%Y A124944 A026794 counts partitions by minimum, strict A026821.
%Y A124944 A325347 counts partitions with integer median, ranks A359908.
%Y A124944 A359893 and A359901 count partitions by median.
%Y A124944 A360005(n)/2 returns median of prime indices.
%Y A124944 Cf. A008289, A025065, A027193, A067538, A237984, A240219, A362608, A363740, A363943, A363944.
%K A124944 nonn,tabl
%O A124944 1,7
%A A124944 _Franklin T. Adams-Watters_, Nov 13 2006