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%I #5 May 18 2019 22:46:27
%S 1,1,0,1,3,2,4,3,7,8,16,15,24,28,39,44,68,80,98,130,167,200,259,320,
%T 396,497,601,737,910,1107,1335,1631,1983,2372,2887,3439,4166,4949,
%U 5940,7043,8450,9980,11884,13984,16679,19493,23162,27050,31937,37334,43926
%N Number of integer partitions of n containing all of their distinct multiplicities.
%C The Heinz numbers of these partitions are given by A325706.
%e 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).
%e The a(0) = 1 through a(10) = 16 partitions:
%e () (1) (21) (22) (41) (51) (61) (71) (81) (91)
%e (31) (221) (321) (421) (431) (333) (541)
%e (211) (2211) (3211) (521) (531) (631)
%e (3111) (3221) (621) (721)
%e (4211) (3321) (3322)
%e (32111) (4221) (3331)
%e (41111) (5211) (4321)
%e (32211) (5221)
%e (6211)
%e (32221)
%e (33211)
%e (42211)
%e (43111)
%e (322111)
%e (421111)
%e (511111)
%t Table[Length[Select[IntegerPartitions[n],SubsetQ[Sort[#],Sort[Length/@Split[#]]]&]],{n,0,30}]
%Y Cf. A109297, A114639, A114640, A181819, A225486, A290689, A324753, A324843, A325702, A325706, A325707, A325755.
%K nonn
%O 0,5
%A _Gus Wiseman_, May 18 2019