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%I #10 Mar 31 2016 09:00:48
%S 0,0,0,1,2,3,5,7,10,15,21,28,38,51,67,89,116,149,192,245,310,393,494,
%T 617,770,956,1181,1457,1790,2190,2675,3257,3952,4788,5784,6968,8380,
%U 10053,12032,14378,17144,20400,24236,28740,34018,40208,47443,55887,65744
%N Number of partitions of n such that the number of even parts is a part.
%e a(10) counts these 21 partitions: 82, 811, 721, 631, 6211, 61111, 541, 5221, 52111, 4321, 43111, 4222, 421111, 4111111, 3322, 33211, 32221, 322111, 3211111, 22111111, 211111111.
%t z = 62; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}]
%Y Cf. A240574, A240575, A240576, A240577, A240578, A240579.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 10 2014