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 A240179 #7 Apr 12 2014 16:21:22
%S A240179 0,1,1,2,4,5,8,11,17,23,33,43,61,79,108,140,187,238,314,397,513,648,
%T A240179 826,1032,1307,1622,2029,2508,3113,3821,4713,5754,7048,8569,10431,
%U A240179 12618,15290,18413,22193,26628,31954,38184,45639,54340,64694,76780,91077,107732
%N A240179 Number of partitions of n such that (least part) <= (multiplicity of greatest part).
%C A240179 Also, for n >= 0, a(n) is the number of partitions of n such that (greatest part) >= (multiplicity of least part). For n >=1, a(n) is also the number of partitions of n such that (least part) >= (multiplicity of greatest part), as well as the number of partitions p of n such that min(p) = min(c(p)), where c = conjugate..
%F A240179 a(n) = A240178(n) + A240180(n), for n >= 0.
%F A240179 2*a(n) + A240180(n) = A000041(n) for n >= 0.
%e A240179 a(6) counts these 8 partitions: 51, 411, 321, 3111, 222, 2211, 21111, 111111.
%t A240179 z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t A240179 Table[Count[f[n], p_ /; Min[p] < Count[p, Max[p]]], {n, 0, z}] (* A240178 *)
%t A240179 Table[Count[f[n], p_ /; Min[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240179 *)
%t A240179 Table[Count[f[n], p_ /; Min[p] == Count[p, Max[p]]], {n, 0, z}] (* A240180 *)
%t A240179 Table[Count[f[n], p_ /; Min[p] > Count[p, Max[p]]], {n, 0, z}] (* A240178, n>0 *)
%t A240179 Table[Count[f[n], p_ /; Min[p] >= Count[p, Max[p]]], {n, 0, z}] (* A240179, n>0 *)
%Y A240179 Cf. A240178, A240180, A000041.
%K A240179 nonn,easy
%O A240179 0,4
%A A240179 _Clark Kimberling_, Apr 02 2014