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A325705
Number of integer partitions of n containing all of their distinct multiplicities.
13
1, 1, 0, 1, 3, 2, 4, 3, 7, 8, 16, 15, 24, 28, 39, 44, 68, 80, 98, 130, 167, 200, 259, 320, 396, 497, 601, 737, 910, 1107, 1335, 1631, 1983, 2372, 2887, 3439, 4166, 4949, 5940, 7043, 8450, 9980, 11884, 13984, 16679, 19493, 23162, 27050, 31937, 37334, 43926
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2019
STATUS
approved