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 A382303 #6 Mar 25 2025 08:57:46
%S A382303 0,0,0,1,1,1,3,2,4,5,8,6,15,13,19,25,33,36,54,58,80,96,122,141,188,
%T A382303 217,274,326,408,474,600,695,859,1012,1233,1440,1763,2050,2475,2899,
%U A382303 3476,4045,4850,5630,6695,7797,9216,10689,12628,14611,17162,19875,23253
%N A382303 Number of integer partitions of n with exactly as many ones as the next greatest multiplicity.
%e A382303 The a(3) = 1 through a(10) = 8 partitions:
%e A382303 (21) (31) (41) (51) (61) (71) (81) (91)
%e A382303 (321) (421) (431) (531) (541)
%e A382303 (2211) (521) (621) (631)
%e A382303 (3311) (32211) (721)
%e A382303 (222111) (4321)
%e A382303 (4411)
%e A382303 (33211)
%e A382303 (42211)
%t A382303 Table[Length[Select[IntegerPartitions[n],Count[#,1]==Max@@Length/@Split[DeleteCases[#,1]]&]],{n,0,30}]
%Y A382303 First differences of A241131, ranks A360013 = 2*A360015 (if we prepend 1).
%Y A382303 The Heinz numbers of these partitions are A360014.
%Y A382303 Equal case of A381544 (ranks A381439).
%Y A382303 A000041 counts integer partitions, strict A000009.
%Y A382303 A008284 counts partitions by length, strict A008289.
%Y A382303 A047993 counts partitions with max = length, ranks A106529.
%Y A382303 A091602 counts partitions by the greatest multiplicity, rank statistic A051903.
%Y A382303 A116598 counts ones in partitions, rank statistic A007814.
%Y A382303 A239964 counts partitions with max multiplicity = length, ranks A212166.
%Y A382303 A240312 counts partitions with max = max multiplicity, ranks A381542.
%Y A382303 A382302 counts partitions with max = max multiplicity = distinct length, ranks A381543.
%Y A382303 Cf. A047966, A051904, A091605, A116861, A237984, A239455, A362608, A363724, A381079, A381437, A381438.
%K A382303 nonn
%O A382303 0,7
%A A382303 _Gus Wiseman_, Mar 24 2025