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%I #7 Apr 29 2014 02:55:44
%S 0,0,0,0,0,1,1,2,3,4,7,10,14,20,27,38,52,70,93,123,161,210,272,350,
%T 447,571,722,911,1144,1430,1782,2213,2736,3374,4146,5082,6208,7567,
%U 9194,11146,13481,16265,19579,23522,28192,33731,40274,47998,57096,67805,80379
%N Number of partitions of n containing m(4) as a part, where m denotes multiplicity.
%e a(10) counts these 7 partitions: 541, 442, 4321, 43111, 42211, 421111, 4111111.
%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, A240490.
%K nonn,easy
%O 0,8
%A _Clark Kimberling_, Apr 06 2014
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