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%I #4 Apr 14 2014 11:13:52
%S 1,0,0,1,0,1,1,2,5,5,7,10,12,17,23,30,35,49,61,78,97,124,155,200,243,
%T 307,375,470,568,710,857,1051,1269,1554,1862,2265,2700,3273,3895,4685,
%U 5558,6658,7883,9394,11084,13167,15493,18336,21517,25367,29703,34914
%N Number of partitions p of n such that the multiplicity of (min(p) + max(p))/2 is a part.
%e a(9) counts these 5 partitions: 531, 333, 3321, 32211, 321111.
%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Min[p]]]], {n, 0, z}] (* A240496 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, (Min[p] + Max[p])/2]]], {n, 1, z}] (* A240497 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]*Max[p]]]], {n, 0, z}] (* A240498 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Length[p]]]], {n, 0, z}] (* A240499 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2*Length[p]]]], {n, 0, z}] (* A240500 *)
%Y Cf. A240496, A240498, A240499, A240500.
%K nonn,easy
%O 1,8
%A _Clark Kimberling_, Apr 06 2014