%I #8 Apr 29 2014 02:57:01
%S 0,1,0,1,2,2,4,5,8,10,16,19,29,36,51,63,89,108,148,182,242,297,390,
%T 475,615,750,955,1161,1466,1774,2217,2679,3316,3994,4911,5892,7197,
%U 8613,10451,12470,15055,17905,21508,25513,30503,36081,42966,50678,60117,70732
%N Number of partitions of n containing m(1) as a part, where m denotes multiplicity.
%e a(6) counts these 5 partitions: 51, 421, 331, 3211, 2221.
%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 1]]], {n, 0, z}] (* A240486 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2]]], {n, 0, z}] (* A240487 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 3]]], {n, 0, z}] (* A240488 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 4]]], {n, 0, z}] (* A240489 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, 5]]], {n, 0, z}] (* A240490 *)
%Y Cf. A240487 - A240490.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Apr 06 2014