%I #7 Apr 29 2014 02:56:25

%S 0,0,0,1,2,2,3,5,7,11,15,20,29,39,51,70,92,119,157,203,259,334,424,

%T 535,678,850,1059,1324,1642,2027,2503,3075,3763,4604,5607,6809,8261,

%U 9988,12043,14508,17424,20879,24988,29835,35548,42303,50232,59544,70491,83297

%N Number of partitions of n containing m(2) as a part, where m denotes multiplicity.

%e a(7) counts these 5 partitions: 421, 322, 3211, 22111, 211111.

%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. A240486 - A240490.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Apr 06 2014