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Number of integer partitions of n > 0 where the maximum part equals the length minus the number of distinct parts.
18

%I #4 Mar 07 2019 23:25:24

%S 0,1,0,0,1,2,2,0,3,1,6,7,7,9,11,10,16,26,22,42,43,54,61,83,85,118,135,

%T 179,201,263,297,371,445,510,608,732,886,1009,1231,1442,1721,2015,

%U 2416,2750,3327,3784,4542,5190,6142,7044,8315,9573,11203,12913,15056

%N Number of integer partitions of n > 0 where the maximum part equals the length minus the number of distinct parts.

%C The Heinz numbers of these integer partitions are given by A324517.

%e The a(2) = 1 through a(12) = 7 integer partitions:

%e (11) (2111) (222) (2221) (33111) (322111) (32222) (3333)

%e (2211) (31111) (321111) (33311) (33222)

%e (411111) (322211) (322221)

%e (332111) (332211)

%e (4211111) (441111)

%e (5111111) (4221111)

%e (4311111)

%t Table[Length[Select[IntegerPartitions[n],Max@@#==Length[#]-Length[Union[#]]&]],{n,30}]

%Y Cf. A003114, A006141, A039900, A046660, A047993, A064174, A106529.

%Y Cf. A324516, A324517, A324520, A324562.

%K nonn

%O 1,6

%A _Gus Wiseman_, Mar 06 2019