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A240183 Number of partitions of n such that (greatest part) = (multiplicity of least part).

%I A240183 #9 Apr 12 2014 16:22:02
%S A240183 0,1,0,0,2,0,2,0,3,3,4,2,9,3,10,10,17,11,26,19,36,33,48,47,79,71,101,
%T A240183 109,149,151,215,216,293,318,404,443,575,611,773,864,1068,1175,1458,
%U A240183 1609,1964,2210,2642,2970,3577,3995,4753,5369,6332,7138,8414,9476
%N A240183 Number of partitions of n such that (greatest part) = (multiplicity of least part).
%F A240183 A240178(n) + a(n) + A240184(n) = A000041(n) for n >= 0.
%e A240183 a(8) counts these 3 partitions:  41111, 32111, 22211.
%t A240183 z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t A240183 t1 = Table[Count[f[n], p_ /; Max[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240178 except for n=0 *)
%t A240183 t2 = Table[Count[f[n], p_ /; Max[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240182 *)
%t A240183 t3 = Table[Count[f[n], p_ /; Max[p] == Count[p, Min[p]]], {n, 0, z}] (* A240183 *)
%t A240183 t4 = Table[Count[f[n], p_ /; Max[p] > Count[p, Min[p]]], {n, 0, z}] (* A240184 *)
%t A240183 t5 = Table[Count[f[n], p_ /; Max[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240179 *)
%Y A240183 Cf. A240178, A240182, A240184, A240179, A000041.
%K A240183 nonn,easy
%O A240183 0,5
%A A240183 _Clark Kimberling_, Apr 02 2014