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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.

A325244 Number of integer partitions of n with one fewer distinct multiplicities than distinct parts.

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%I A325244 #5 Apr 16 2019 15:26:49
%S A325244 0,0,0,1,1,2,3,4,7,12,16,21,33,38,50,75,87,111,150,185,244,307,373,
%T A325244 461,585,702,856,1043,1255,1498,1822,2143,2565,3064,3607,4251,5064,
%U A325244 5920,6953,8174,9503,11064,12927,14921,17320,19986,23067,26485,30499,34894
%N A325244 Number of integer partitions of n with one fewer distinct multiplicities than distinct parts.
%C A325244 For example, (32211) has two distinct multiplicities (1, 2) and three distinct parts (1, 2, 3) so is counted under a(9).
%C A325244 The Heinz numbers of these partitions are given by A325259.
%e A325244 The a(3) = 1 through a(10) = 16 partitions:
%e A325244   (21)  (31)  (32)  (42)    (43)    (53)     (54)      (64)
%e A325244               (41)  (51)    (52)    (62)     (63)      (73)
%e A325244                     (2211)  (61)    (71)     (72)      (82)
%e A325244                             (3211)  (3221)   (81)      (91)
%e A325244                                     (3311)   (3321)    (3322)
%e A325244                                     (4211)   (4221)    (4411)
%e A325244                                     (32111)  (4311)    (5221)
%e A325244                                              (5211)    (5311)
%e A325244                                              (32211)   (6211)
%e A325244                                              (42111)   (32221)
%e A325244                                              (222111)  (33211)
%e A325244                                              (321111)  (42211)
%e A325244                                                        (43111)
%e A325244                                                        (52111)
%e A325244                                                        (421111)
%e A325244                                                        (3211111)
%t A325244 Table[Length[Select[IntegerPartitions[n],Length[Union[#]]==Length[Union[Length/@Split[#]]]+1&]],{n,0,30}]
%Y A325244 Cf. A008284, A071625, A090858, A098859, A116608, A117571, A127002, A325242, A325259, A325270.
%K A325244 nonn
%O A325244 0,6
%A A325244 _Gus Wiseman_, Apr 15 2019