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%I #5 Apr 12 2014 16:22:32
%S 0,0,1,1,1,2,3,3,4,5,7,9,11,14,17,21,24,33,37,47,56,67,79,100,109,137,
%T 161,189,217,272,297,365,416,485,560,685,726,891,1029,1176,1314,1600,
%U 1728,2085,2336,2637,3020,3621,3802,4554,5171,5820,6461,7691,8266
%N Number of partitions p of n such that mean(p) < multiplicity(max(p)).
%F a(n) = A240201(n) - A116900(n) for n >= 0.
%F a(n) + A116900(n) + A240202(n) = A000041(n) for n >= 1.
%e a(6) counts these 3 partitions: 222, 2211, 111111.
%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
%t t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Max[p]]], {n, 0, z}] (* A240200 *)
%t t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Max[p]]], {n, 0, z}] (* A240201 *)
%t t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Max[p]]], {n, 0, z}] (* A116900 *)
%t t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Max[p]]], {n, 0, z}] (* A240202 *)
%t t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Max[p]]], {n, 0, z}] (* A116901 *)
%Y Cf. A240201, A240202, A116900, A116901, A000041.
%K nonn,easy
%O 0,6
%A _Clark Kimberling_, Apr 03 2014
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