OFFSET
0,5
COMMENTS
The Heinz numbers of these partitions are given by A325706.
EXAMPLE
The partition (4,2,1,1,1,1) has distinct multiplicities {1,4}, both of which belong to the partition, so it is counted under a(10).
The a(0) = 1 through a(10) = 16 partitions:
() (1) (21) (22) (41) (51) (61) (71) (81) (91)
(31) (221) (321) (421) (431) (333) (541)
(211) (2211) (3211) (521) (531) (631)
(3111) (3221) (621) (721)
(4211) (3321) (3322)
(32111) (4221) (3331)
(41111) (5211) (4321)
(32211) (5221)
(6211)
(32221)
(33211)
(42211)
(43111)
(322111)
(421111)
(511111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], SubsetQ[Sort[#], Sort[Length/@Split[#]]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2019
STATUS
approved