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 A361800 #15 Apr 22 2023 09:28:05
%S A361800 1,0,0,2,0,0,1,2,3,3,3,3,4,6,9,13,14,15,18,21,27,32,40,46,55,62,72,82,
%T A361800 95,111,131,157,186,225,264,316,366,430,495,578,663,768,880,1011,1151,
%U A361800 1316,1489,1690,1910,2158,2432,2751,3100,3505,3964,4486,5079,5764
%N A361800 Number of integer partitions of n with the same length as median.
%C A361800 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 A361800 The a(1) = 1 through a(15) = 9 partitions (A=10, B=11):
%e A361800 1 . . 22 . . 331 332 333 433 533 633 733 833 933
%e A361800 31 431 432 532 632 732 832 932 A32
%e A361800 531 631 731 831 931 A31 B31
%e A361800 4441 4442 4443
%e A361800 5441 5442
%e A361800 5531 5532
%e A361800 6441
%e A361800 6531
%e A361800 6621
%t A361800 Table[Length[Select[IntegerPartitions[n],Length[#]==Median[#]&]],{n,30}]
%Y A361800 For minimum instead of median we have A006141, for twice minimum A237757.
%Y A361800 For maximum instead of median we have A047993, for twice length A237753.
%Y A361800 For maximum instead of length we have A053263, for twice median A361849.
%Y A361800 For mean instead of median we have A206240 (zeros removed).
%Y A361800 For minimum instead of length we have A361860.
%Y A361800 For twice median we have A362049, ranks A362050.
%Y A361800 A000041 counts integer partitions, strict A000009.
%Y A361800 A000975 counts subsets with integer median.
%Y A361800 A325347 counts partitions with integer median, complement A307683.
%Y A361800 A359893 and A359901 count partitions by median.
%Y A361800 A360005 gives twice median of prime indices.
%Y A361800 Cf. A008284, A013580, A027193, A079309, A240219, A362048.
%K A361800 nonn
%O A361800 1,4
%A A361800 _Gus Wiseman_, Apr 07 2023