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 A325242 #10 Apr 16 2019 18:32:10 %S A325242 1,2,3,4,1,4,3,8,3,6,9,10,12,11,19,15,26,1,13,39,4,25,47,5,19,70,12, %T A325242 29,89,17,33,115,28,42,148,41,39,189,69,62,235,88,55,294,141,81,362, %U A325242 183,1,84,450,253,5,103,558,333,8,105,669,464,17,153,817,576,29 %N A325242 Irregular triangle read by rows with zeros removed where T(n,k) is the number of integer partitions of n with k distinct multiplicities, n > 0. %C A325242 For example, the partition (32111) has multiplicities {1,1,3}, of which 2 are distinct, so is counted under T(8,2). %H A325242 Alois P. Heinz, <a href="/A325242/b325242.txt">Rows n = 1..200, flattened</a> %e A325242 Triangle begins: %e A325242 1 %e A325242 2 %e A325242 3 %e A325242 4 1 %e A325242 4 3 %e A325242 8 3 %e A325242 6 9 %e A325242 10 12 %e A325242 11 19 %e A325242 15 26 1 %e A325242 13 39 4 %e A325242 25 47 5 %e A325242 19 70 12 %e A325242 29 89 17 %e A325242 33 115 28 %e A325242 42 148 41 %e A325242 39 189 69 %e A325242 62 235 88 %e A325242 55 294 141 %e A325242 81 362 183 1 %e A325242 Row n = 8 counts the following partitions: %e A325242 (8) (332) %e A325242 (44) (422) %e A325242 (53) (611) %e A325242 (62) (3221) %e A325242 (71) (4211) %e A325242 (431) (5111) %e A325242 (521) (22211) %e A325242 (2222) (32111) %e A325242 (3311) (41111) %e A325242 (11111111) (221111) %e A325242 (311111) %e A325242 (2111111) %t A325242 DeleteCases[Table[Length[Select[IntegerPartitions[n],Length[Union[Length/@Split[#]]]==k&]],{n,20},{k,n}],0,2] %Y A325242 Row lengths are A056556. Row sums are A000041. Column k = 1 is A047966. Column k = 2 is A325243. %Y A325242 Cf. A008284, A062770, A071625, A098859, A116608, A127002, A183558, A243978, A244515, A325244, A325268. %K A325242 nonn,tabf %O A325242 1,2 %A A325242 _Gus Wiseman_, Apr 15 2019