%I #5 May 03 2014 11:25:42

%S 0,0,0,1,1,3,5,7,12,17,26,34,49,66,90,118,155,203,261,337,428,546,685,

%T 863,1075,1345,1664,2060,2538,3118,3816,4661,5680,6901,8368,10111,

%U 12207,14690,17656,21155,25326,30238,36058,42901,50973,60438,71568,84586

%N Number of partitions p of n such that (number of even numbers in p) is a part of p.

%C Each number in p is counted once, regardless of its multiplicity.

%e a(6) counts these 5 partitions: 42, 411, 321, 2211, 21111.

%t z = 50; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2], 0]; s1[p_] :=

%t Count[Mod[DeleteDuplicates[p], 2], 1];

%t Table[Count[f[n], p_ /; MemberQ[p, s0[p]]], {n, 0, z}] (* A241544 *)

%t Table[Count[f[n], p_ /; MemberQ[p, s1[p]]], {n, 0, z}] (* A241545 *)

%Y Cf. A241545.

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Apr 26 2014