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 A363726 #8 Jun 27 2023 19:41:16
%S A363726 0,1,1,2,2,4,4,7,8,12,14,22,26,39,50,67,86,118,148,196,245,315,394,
%T A363726 507,629,792,979,1231,1503,1873,2286,2814,3424,4194,5073,6183,7449,
%U A363726 9014,10827,13055,15603,18713,22308,26631,31646,37641,44559,52835,62374,73671
%N A363726 Number of odd-length integer partitions of n with a unique mode.
%C A363726 A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes in {a,a,b,b,b,c,d,d,d} are {b,d}.
%e A363726 The a(1) = 1 through a(8) = 8 partitions:
%e A363726 (1) (2) (3) (4) (5) (6) (7) (8)
%e A363726 (111) (211) (221) (222) (322) (332)
%e A363726 (311) (411) (331) (422)
%e A363726 (11111) (21111) (511) (611)
%e A363726 (22111) (22211)
%e A363726 (31111) (32111)
%e A363726 (1111111) (41111)
%e A363726 (2111111)
%t A363726 modes[ms_]:=Select[Union[ms],Count[ms,#]>=Max@@Length/@Split[ms]&];
%t A363726 Table[Length[Select[IntegerPartitions[n], Length[modes[#]]==1&&OddQ[Length[#]]&]],{n,30}]
%Y A363726 The constant case is A001227.
%Y A363726 Allowing multiple modes gives A027193, ranks A026424.
%Y A363726 Allowing any length gives A362608, ranks A356862.
%Y A363726 A000041 counts partitions, strict A000009.
%Y A363726 A008284 counts partitions by length (or decreasing mean), strict A008289.
%Y A363726 A359893 and A359901 count partitions by median.
%Y A363726 Cf. A325347, A363719, A363720, A363731, A363724, A363725, A363740.
%K A363726 nonn
%O A363726 0,4
%A A363726 _Gus Wiseman_, Jun 27 2023