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Number of integer partitions of n > 0 where the minimum part equals the number of parts minus the number of distinct parts.
16

%I #5 Mar 07 2019 23:25:42

%S 0,1,0,1,2,2,3,3,7,6,11,12,15,21,25,31,43,49,58,79,89,108,135,165,190,

%T 232,279,328,387,461,536,650,743,870,1029,1202,1381,1613,1864,2163,

%U 2505,2875,3292,3829,4367,5001,5746,6538,7462,8533,9714,11008,12527,14196

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

%C The Heinz numbers of these integer partitions are given by A324519.

%e The a(2) = 1 through a(11) = 11 integer partitions:

%e (11) (211) (221) (222) (331) (611) (441) (811) (551)

%e (311) (411) (511) (3221) (711) (3322) (911)

%e (3211) (4211) (3222) (4222) (3332)

%e (3321) (5221) (4331)

%e (4221) (5311) (4421)

%e (4311) (6211) (5222)

%e (5211) (5411)

%e (6221)

%e (6311)

%e (7211)

%e (43211)

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

%Y Cf. A003114, A006141, A039900, A046660, A047993, A064174, A090858, A133121.

%Y Cf. A324516, A324518, A324519, A324520.

%K nonn

%O 1,5

%A _Gus Wiseman_, Mar 06 2019