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 A325329 #4 May 02 2019 08:52:47
%S A325329 1,1,2,3,4,4,8,7,13,18,25,30,52,57,81,109,140,167,230,267,354,428,532,
%T A325329 630,815,942,1166,1385,1695,1966,2440,2810,3422,4008,4828,5630,6847,
%U A325329 7905,9527,11135,13340,15498,18636,21591,25769,30086,35630,41379,49150,56880
%N A325329 Number of integer partitions of n whose multiplicities appear with distinct multiplicities.
%C A325329 The Heinz numbers of these partitions are given by A325369.
%C A325329 Partitions whose parts appear with distinct multiplicities are counted by A098859, with Heinz numbers A130091.
%e A325329 The a(0) = 1 through a(8) = 13 partitions:
%e A325329 () (1) (2) (3) (4) (5) (6) (7) (8)
%e A325329 (11) (21) (22) (32) (33) (43) (44)
%e A325329 (111) (31) (41) (42) (52) (53)
%e A325329 (1111) (11111) (51) (61) (62)
%e A325329 (222) (421) (71)
%e A325329 (321) (3211) (431)
%e A325329 (2211) (1111111) (521)
%e A325329 (111111) (2222)
%e A325329 (3221)
%e A325329 (3311)
%e A325329 (4211)
%e A325329 (32111)
%e A325329 (11111111)
%e A325329 For example, in (4,2,1,1), the multiplicities are 1 and 2, and 2 appears 1 time while 1 appears 2 times, so (4,2,1,1) is counted under a(8).
%t A325329 Table[Length[Select[IntegerPartitions[n],UnsameQ@@Length/@Split[Sort[Length/@Split[#]]]&]],{n,0,30}]
%Y A325329 Cf. A098859, A130091, A317081, A320348, A325326, A325330, A325331, A325333, A325337, A325369.
%K A325329 nonn
%O A325329 0,3
%A A325329 _Gus Wiseman_, May 01 2019