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 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