OFFSET
0,5
COMMENTS
The Heinz numbers of these partitions are given by A325755.
EXAMPLE
The partition x = (4,3,1,1,1) has multiplicities (3,1,1), which are a submultiset of x, so x is counted under a(10).
The a(1) = 1 through a(11) = 7 partitions:
(1) (22) (221) (2211) (3211) (4211) (333) (3322) (7211)
(211) (3111) (32111) (5211) (3331) (33221)
(41111) (32211) (6211) (52211)
(42211) (53111)
(43111) (322211)
(322111) (332111)
(421111) (431111)
(511111)
MATHEMATICA
submultQ[cap_, fat_]:=And@@Function[i, Count[fat, i]>=Count[cap, i]]/@Union[List@@cap]
Table[Length[Select[IntegerPartitions[n], submultQ[Sort[Length/@Split[#]], #]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2019
STATUS
approved