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 A360456 #6 Feb 11 2023 08:13:06
%S A360456 1,1,0,0,1,0,0,1,2,5,7,10,14,21,28,36,51,64,84,106,132,165,202,252,
%T A360456 311,391,473,579,713,868,1069,1303,1617,1954,2404,2908,3556,4282,5200,
%U A360456 6207,7505,8934,10700,12717,15165,17863,21222,24976,29443,34523,40582,47415
%N A360456 Number of integer partitions of n for which the parts have the same median as the multiplicities.
%C A360456 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 A360456 The a(1) = 1 through a(11) = 10 partitions:
%e A360456 1 . . 22 . . 2221 3311 333 4222 5222
%e A360456 32111 3222 33211 33221
%e A360456 32211 42211 52211
%e A360456 42111 43111 53111
%e A360456 321111 52111 62111
%e A360456 421111 322211
%e A360456 3211111 431111
%e A360456 521111
%e A360456 4211111
%e A360456 32111111
%t A360456 Table[Length[Select[IntegerPartitions[n], Median[Length/@Split[#]]==Median[#]&]],{n,0,30}]
%Y A360456 For mean instead of median: A360068, ranks A359903.
%Y A360456 For distinct parts instead of multiplicities: A360245, ranks A360249.
%Y A360456 These partitions have ranks A360454.
%Y A360456 For distinct parts instead of parts: A360455, ranks A360453.
%Y A360456 A000041 counts integer partitions, strict A000009.
%Y A360456 A008284 counts partitions by number of parts.
%Y A360456 A325347 counts partitions w/ integer median, strict A359907, ranks A359908.
%Y A360456 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360456 Cf. A000975, A027193, A114638, A240219, A359894, A359895, A360244, A360248.
%K A360456 nonn
%O A360456 0,9
%A A360456 _Gus Wiseman_, Feb 10 2023