A324518 Number of integer partitions of n > 0 where the maximum part equals the length minus the number of distinct parts.

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, 179, 201, 263, 297, 371, 445, 510, 608, 732, 886, 1009, 1231, 1442, 1721, 2015, 2416, 2750, 3327, 3784, 4542, 5190, 6142, 7044, 8315, 9573, 11203, 12913, 15056

Offset: 1

Author

Gus Wiseman, Mar 06 2019

Keywords

• nonn

Comments

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

Examples

			The a(2) = 1 through a(12) = 7 integer partitions:
  (11)  (2111)  (222)   (2221)   (33111)   (322111)  (32222)    (3333)
                (2211)  (31111)  (321111)            (33311)    (33222)
                                 (411111)            (322211)   (322221)
                                                     (332111)   (332211)
                                                     (4211111)  (441111)
                                                     (5111111)  (4221111)
                                                                (4311111)
		

Crossrefs

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

Cf. A324516, A324517, A324520, A324562.

Programs

Mathematica

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