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Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal.
29

%I #15 Jul 07 2020 06:07:02

%S 1,1,0,0,2,1,1,0,1,1,3,2,3,3,5,0,4,5,2,3,8,6,5,10,9,9,16,14,12,16,17,

%T 10,17,15,16,19,35,17,34,37,40,31,54,36,60,61,58,63,88,58,88,87,91,84,

%U 115,93,116,108,115,130,190,143,165,214,219,200,255,240

%N Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal.

%C The Heinz numbers of these partitions are given by A109297. - _Gus Wiseman_, Apr 02 2019

%e From _Gus Wiseman_, Apr 02 2019: (Start)

%e The initial terms count the following integer partitions:

%e 0: ()

%e 1: (1)

%e 4: (22)

%e 4: (211)

%e 5: (221)

%e 6: (3111)

%e 8: (41111)

%e 9: (333)

%e 10: (511111)

%e 10: (3331)

%e 10: (322111)

%e 11: (332111)

%e 11: (322211)

%e 12: (6111111)

%e 12: (4221111)

%e 12: (33222)

%e 13: (33322)

%e 13: (333211)

%e 13: (332221)

%e 14: (71111111)

%e 14: (52211111)

%e 14: (4421111)

%e 14: (4222211)

%e 14: (333221)

%e (End)

%t Table[Length[Select[IntegerPartitions[n],Union[#]==Union[Length/@Split[#]]&]],{n,0,30}] (* _Gus Wiseman_, Apr 02 2019 *)

%Y Cf. A052335, A087153, A109297, A114639, A115584, A117144, A276429, A324572, A325132, A336031.

%K nonn

%O 0,5

%A _Vladeta Jovovic_, Feb 18 2006

%E More terms from _Alois P. Heinz_, Aug 09 2016