%I #7 Apr 19 2019 08:10:16

%S 0,0,0,0,1,2,1,5,6,9,10,18,18,31,34,48,57,80,86,122,138,183,211,275,

%T 311,402,461,576,663,825,942,1163,1334,1621,1865,2248,2566,3084,3532,

%U 4193,4794,5674,6472,7617,8685,10153,11576,13483,15320,17790,20200,23342

%N Number of integer partitions of n whose maximum multiplicity is one greater than their minimum multiplicity.

%C The Heinz numbers of these partitions are given by A325241.

%C For example, the partition (44111) has two multiplicities (2 and 3) which differ by 1, so is counted under a(11).

%e The a(4) = 1 through a(11) = 18 partitions:

%e (211) (221) (411) (322) (332) (441) (433) (443)

%e (311) (331) (422) (522) (442) (533)

%e (511) (611) (711) (622) (551)

%e (3211) (3221) (3321) (811) (722)

%e (22111) (4211) (4221) (5221) (911)

%e (22211) (4311) (5311) (4322)

%e (5211) (6211) (4331)

%e (32211) (33211) (4421)

%e (33111) (42211) (5411)

%e (2221111) (6221)

%e (6311)

%e (7211)

%e (33221)

%e (33311)

%e (43211)

%e (44111)

%e (52211)

%e (2222111)

%t Table[Length[Select[IntegerPartitions[n],Max@@Length/@Split[#]-Min@@Length/@Split[#]==1&]],{n,0,30}]

%Y Cf. A047966, A062770, A071625, A098859, A117571, A127002, A325242, A325244, A325245, A325280.

%K nonn

%O 0,6

%A _Gus Wiseman_, Apr 18 2019