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%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