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%I #8 Apr 22 2014 01:31:19
%S 0,0,1,1,2,2,3,3,5,5,7,7,11,11,15,16,22,23,31,32,42,45,58,62,79,84,
%T 106,114,140,151,187,201,244,265,319,346,413,449,533,580,683,744,873,
%U 951,1106,1209,1400,1529,1764,1927,2212,2418,2763,3021,3442,3763,4270
%N Number of partitions of n into distinct parts of which the number of odd parts is not a part.
%F a(n) + A240574(n) = A000009(n) for n >= 1.
%e a(9) counts these 5 partitions: 9, 72, 63, 54, 432.
%t z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t t1 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}] (* A240869 *)
%t t2 = Table[Count[f[n], p_ /; ! MemberQ[p, Count[Mod[p, 2], 1]]], {n, 0, z}] (* A240870 *)
%Y Cf. A240869, A240573, A000009.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 14 2014