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 A240305 #5 Apr 14 2014 11:09:11
%S A240305 1,0,0,1,1,2,3,5,7,12,14,21,29,38,50,70,90,117,156,196,253,324,411,
%T A240305 514,650,809,1015,1259,1555,1917,2365,2898,3536,4318,5248,6365,7691,
%U A240305 9297,11180,13446,16115,19296,23019,27474,32653,38838,46002,54511,64371,76012
%N A240305 Number of partitions p of n such that (maximal multiplicity of the parts of p) < (number of distinct parts of p).
%F A240305 a(n) = A240306(n) - A239964(n) for n >= 0.
%F A240305 a(n) + A239964(n) + A240309(n) = A000041(n) for n >= 0.
%e A240305 a(6) counts these 3 partitions: 51, 42, 321.
%t A240305 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 A240305 t1 = Table[Count[f[n], p_ /; m[p] < d[p]], {n, 0, z}] (* A240305 *)
%t A240305 t2 = Table[Count[f[n], p_ /; m[p] <= d[p]], {n, 0, z}] (* A240306 *)
%t A240305 t3 = Table[Count[f[n], p_ /; m[p] == d[p]], {n, 0, z}] (* A239964 *)
%t A240305 t4 = Table[Count[f[n], p_ /; m[p] >= d[p]], {n, 0, z}] (* A240308 *)
%t A240305 t5 = Table[Count[f[n], p_ /; m[p] > d[p]], {n, 0, z}] (* A240309 *)
%Y A240305 Cf. A240306, A239964, A240308, A240309, A000041.
%K A240305 nonn,easy
%O A240305 0,6
%A A240305 _Clark Kimberling_, Apr 05 2014