This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325705 #5 May 18 2019 22:46:27
%S A325705 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 A325705 396,497,601,737,910,1107,1335,1631,1983,2372,2887,3439,4166,4949,
%U A325705 5940,7043,8450,9980,11884,13984,16679,19493,23162,27050,31937,37334,43926
%N A325705 Number of integer partitions of n containing all of their distinct multiplicities.
%C A325705 The Heinz numbers of these partitions are given by A325706.
%e A325705 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 A325705 The a(0) = 1 through a(10) = 16 partitions:
%e A325705 () (1) (21) (22) (41) (51) (61) (71) (81) (91)
%e A325705 (31) (221) (321) (421) (431) (333) (541)
%e A325705 (211) (2211) (3211) (521) (531) (631)
%e A325705 (3111) (3221) (621) (721)
%e A325705 (4211) (3321) (3322)
%e A325705 (32111) (4221) (3331)
%e A325705 (41111) (5211) (4321)
%e A325705 (32211) (5221)
%e A325705 (6211)
%e A325705 (32221)
%e A325705 (33211)
%e A325705 (42211)
%e A325705 (43111)
%e A325705 (322111)
%e A325705 (421111)
%e A325705 (511111)
%t A325705 Table[Length[Select[IntegerPartitions[n],SubsetQ[Sort[#],Sort[Length/@Split[#]]]&]],{n,0,30}]
%Y A325705 Cf. A109297, A114639, A114640, A181819, A225486, A290689, A324753, A324843, A325702, A325706, A325707, A325755.
%K A325705 nonn
%O A325705 0,5
%A A325705 _Gus Wiseman_, May 18 2019