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 A363262 #7 Jun 06 2023 08:17:57
%S A363262 0,1,1,2,4,9,18,37,73,145,287,570,1134,2264,4526,9061,18152,36374,
%T A363262 72884,146011,292416,585422,1171632,2344136,4688821,9376832,18749169,
%U A363262 37485358,74939850,149813328,299492966,598729533,1196987066,2393137399,4784846896,9567357951
%N A363262 Number of integer compositions of n in which the greatest part appears more than once.
%C A363262 Also the number of multisets of length n covering an initial interval of positive integers with more than one mode.
%e A363262 The a(2) = 1 through a(6) = 9 compositions:
%e A363262 (11) (111) (22) (122) (33)
%e A363262 (1111) (212) (222)
%e A363262 (221) (1122)
%e A363262 (11111) (1212)
%e A363262 (1221)
%e A363262 (2112)
%e A363262 (2121)
%e A363262 (2211)
%e A363262 (111111)
%t A363262 Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n],Count[#,Max@@#]>1&]],{n,15}]
%Y A363262 For partitions instead of compositions we have A002865.
%Y A363262 The complement is counted by A097979 shifted left.
%Y A363262 Row sums of columns k > 1 of A238341.
%Y A363262 If all parts appear more than once we have A240085, for partitions A007690.
%Y A363262 If the greatest part appears exactly twice we have A243737.
%Y A363262 For least instead of greatest we have A363224, see triangle A238342.
%Y A363262 A000041 counts integer partitions, strict A000009.
%Y A363262 A032020 counts strict compositions.
%Y A363262 A067029 gives last exponent in prime factorization, first A071178.
%Y A363262 A261982 counts compositions with some part appearing more than once.
%Y A363262 Cf. A008284, A105039, A117989, A362607, A362608, A362612, A362614.
%K A363262 nonn
%O A363262 1,4
%A A363262 _Gus Wiseman_, Jun 04 2023