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%I #7 Apr 29 2014 02:55:11
%S 0,0,0,0,0,0,1,1,2,3,5,6,11,14,21,28,40,51,73,93,126,162,215,271,357,
%T 449,578,725,923,1146,1447,1788,2232,2747,3403,4160,5123,6234,7620,
%U 9236,11227,13540,16381,19678,23682,28348,33969,40501,48346,57449,68302
%N Number of partitions of n containing m(5) as a part, where m denotes multiplicity.
%e a(12) counts these 11 partitions: 651, 552, 5421, 54111, 5331, 53211, 531111, 52221, 522111, 5211111, 51111111.
%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, A240487, A240488, A240489.
%K nonn,easy
%O 0,9
%A _Clark Kimberling_, Apr 06 2014
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