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 A363484 #8 Jun 07 2023 08:31:52
%S A363484 0,1,1,1,2,3,2,5,6,6,8,11,12,17,20,21,27,35,38,50,56,65,76,95,105,125,
%T A363484 146,167,198,233,252,305,351,394,457,522,585,681,778,878,994,1135,
%U A363484 1269,1446,1638,1828,2067,2339,2613,2940,3301,3684,4143,4634,5156,5771
%N A363484 Number of integer partitions of n covering an initial interval of positive integers with a unique mode.
%C A363484 A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes of {a,a,b,b,b,c,d,d,d} are {b,d}.
%e A363484 The a(1) = 1 through a(8) = 6 partitions:
%e A363484 (1) (11) (111) (211) (221) (21111) (2221) (3221)
%e A363484 (1111) (2111) (111111) (3211) (22211)
%e A363484 (11111) (22111) (32111)
%e A363484 (211111) (221111)
%e A363484 (1111111) (2111111)
%e A363484 (11111111)
%t A363484 Table[If[n==0,0,Length[Select[IntegerPartitions[n], Union[#]==Range[Max@@#]&&Length[Commonest[#]]==1&]]],{n,0,30}]
%Y A363484 For parts instead of multiplicities we have A096765, complement A025147.
%Y A363484 For multisets instead of partitions we have A097979, complement A363262.
%Y A363484 For co-mode we have A363263, complement A363264.
%Y A363484 The complement is counted by A363485.
%Y A363484 A000041 counts integer partitions, A000009 covering an initial interval.
%Y A363484 A362607 counts partitions with multiple modes, co-modes A362609.
%Y A363484 A362608 counts partitions with a unique mode, co-mode A362610.
%Y A363484 A362614 counts partitions by number of modes, co-modes A362615.
%Y A363484 Cf. A002865, A008284, A105039, A117989, A243737, A362612.
%K A363484 nonn
%O A363484 0,5
%A A363484 _Gus Wiseman_, Jun 05 2023