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 A240309 #4 Apr 14 2014 11:10:00
%S A240309 0,0,1,1,2,2,5,6,9,13,17,23,33,42,59,76,100,128,173,212,275,350,447,
%T A240309 552,704,870,1094,1346,1672,2048,2540,3084,3775,4595,5592,6764,8180,
%U A240309 9853,11865,14250,17075,20404,24376,29024,34498,41012,48550,57463,67873
%N A240309 Number of partitions p of n such that (maximal multiplicity of the parts of p) > (number of distinct parts of p).
%F A240309 a(n) = A240308(n) - A239964(n) for n >= 0.
%F A240309 a(n) + A240305(n) + A239964(n) = A000041(n) for n >= 0.
%e A240309 a(6) counts these 5 partitions: 33, 3111, 222, 21111, 111111.
%t A240309 z = 60; f[n_] := f[n] = IntegerPartitions[n]; m[p_] := Max[Map[Length, Split[p]]] (* maximal multiplicity *); d[p_] := d[p] = Length[DeleteDuplicates[p]] (* number of distinct terms *)
%t A240309 t1 = Table[Count[f[n], p_ /; m[p] < d[p]], {n, 0, z}] (* A240305 *)
%t A240309 t2 = Table[Count[f[n], p_ /; m[p] <= d[p]], {n, 0, z}] (* A240306 *)
%t A240309 t3 = Table[Count[f[n], p_ /; m[p] == d[p]], {n, 0, z}] (* A239964 *)
%t A240309 t4 = Table[Count[f[n], p_ /; m[p] >= d[p]], {n, 0, z}] (* A240308 *)
%t A240309 t5 = Table[Count[f[n], p_ /; m[p] > d[p]], {n, 0, z}] (* A240309 *)
%Y A240309 Cf. A240305, A240306, A239964, A240308, A000041.
%K A240309 nonn,easy
%O A240309 0,5
%A A240309 _Clark Kimberling_, Apr 05 2014