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Number of partitions p of n such that min(p) < (number of parts of p) <= max(p).
3

%I #7 Apr 23 2019 23:58:11

%S 0,0,1,1,2,3,6,8,12,17,24,33,46,61,82,108,142,184,239,305,391,495,626,

%T 786,985,1226,1524,1884,2323,2853,3497,4268,5200,6314,7650,9243,11146,

%U 13403,16090,19268,23032,27473,32716,38878,46130,54633,64603,76264,89899

%N Number of partitions p of n such that min(p) < (number of parts of p) <= max(p).

%e a(7) counts these 6 partitions: {6,1}, {5,1,1}, {4,2,1}, {4,1,1,1}, {3,3,1}, {3,2,2}.

%t Table[Count[IntegerPartitions[n], q_ /; Min[q] < Length[q] <= Max[q]], {n, 60}]

%Y Cf. A000041, A325340, A325341, A325343.

%K nonn,easy

%O 1,5

%A _Clark Kimberling_, Apr 21 2019