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%I #4 Apr 17 2014 14:29:29
%S 0,1,0,1,1,3,2,4,4,11,9,16,15,30,29,48,49,81,82,125,136,203,220,306,
%T 344,476,537,710,822,1068,1240,1565,1851,2305,2733,3323,3989,4796,
%U 5775,6826,8287,9694,11787,13611,16659,19070,23363,26463,32554,36616,45080
%N Number of partitions n such that the multiplicity of the number of odd parts is a part.
%e a(7) counts these 4 partitions: 61, 421, 3211, 2221; e.g., 3211 has 3 odd parts, and the multiplicity of 3 is 1, which is a part of 3211.
%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Count[Mod[p, 2], 0]]]], {n, 0, z}] (* A240540 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Count[Mod[p, 2], 1]]]], {n, 0, z}] (* A240541 *)
%Y Cf. A240540.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 07 2014
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