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%I #5 Apr 16 2019 15:26:49
%S 0,0,0,1,1,2,3,4,7,12,16,21,33,38,50,75,87,111,150,185,244,307,373,
%T 461,585,702,856,1043,1255,1498,1822,2143,2565,3064,3607,4251,5064,
%U 5920,6953,8174,9503,11064,12927,14921,17320,19986,23067,26485,30499,34894
%N Number of integer partitions of n with one fewer distinct multiplicities than distinct parts.
%C For example, (32211) has two distinct multiplicities (1, 2) and three distinct parts (1, 2, 3) so is counted under a(9).
%C The Heinz numbers of these partitions are given by A325259.
%e The a(3) = 1 through a(10) = 16 partitions:
%e (21) (31) (32) (42) (43) (53) (54) (64)
%e (41) (51) (52) (62) (63) (73)
%e (2211) (61) (71) (72) (82)
%e (3211) (3221) (81) (91)
%e (3311) (3321) (3322)
%e (4211) (4221) (4411)
%e (32111) (4311) (5221)
%e (5211) (5311)
%e (32211) (6211)
%e (42111) (32221)
%e (222111) (33211)
%e (321111) (42211)
%e (43111)
%e (52111)
%e (421111)
%e (3211111)
%t Table[Length[Select[IntegerPartitions[n],Length[Union[#]]==Length[Union[Length/@Split[#]]]+1&]],{n,0,30}]
%Y Cf. A008284, A071625, A090858, A098859, A116608, A117571, A127002, A325242, A325259, A325270.
%K nonn
%O 0,6
%A _Gus Wiseman_, Apr 15 2019
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