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Number of partitions of n such that the multiplicity of the greatest part is a part.

5

`%I #6 Aug 01 2014 13:42:00
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`%S 0,1,0,1,3,4,6,8,13,18,27,36,51,67,92,120,162,208,276,352,457,579,743,
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`%T 931,1183,1474,1851,2293,2857,3515,4347,5320,6532,7955,9708,11762,
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`%U 14279,17224,20798,24986,30034,35935,43012,51274,61125,72617,86249,102120
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`%N Number of partitions of n such that the multiplicity of the greatest part is a part.
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`%e a(6) counts these 6 partitions: 51, 411, 321, 3111, 2211, 21111.
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`%t z = 60; f[n_] := f[n] = IntegerPartitions[n];
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`%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Mean[p]]]], {n, 0, z}] (* A240491 *)
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`%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Median[p]]]], {n, 0, z}] (* A240492 *)
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`%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Min[p]]]], {n, 0, z}] (* A240493 *)
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`%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p]]]], {n, 0, z}] (* A240494 *)
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`%t Table[Count[f[n], p_ /; MemberQ[p, Count[p, Max[p] - Min[p]]]], {n, 0, z}] (* A240495 *)
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`%Y Cf. A240491 - A240495.
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`%K nonn,easy
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`%O 0,5
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`%A _Clark Kimberling_, Apr 06 2014
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