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 A353741 #12 Jan 05 2024 13:26:29
%S A353741 1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,1,2,1,2,2,1,1,1,1,2,1,2,1,2,1,
%T A353741 1,2,1,1,1,2,1,2,1,3,1,1,3,1,3,1,1,1,1,2,1,2,1,3,2,1,3,1,1,3,2,2,2,1,
%U A353741 1,1,1,2,1,2,1,3,2,2,3,1,1,4,2,2,1,4,1,1,1,3,2
%N A353741 Irregular triangle read by rows where T(n,k) is the number of integer partitions of n with product k, all zeros removed.
%C A353741 Warning: There are certain internal "holes" in A339095 that are removed in this sequence.
%e A353741 Triangle begins:
%e A353741 1
%e A353741 1
%e A353741 1 1
%e A353741 1 1 1
%e A353741 1 1 1 2
%e A353741 1 1 1 2 1 1
%e A353741 1 1 1 2 1 2 2 1
%e A353741 1 1 1 2 1 2 1 2 1 1 2
%e A353741 1 1 1 2 1 2 1 3 1 1 3 1 3 1
%e A353741 1 1 1 2 1 2 1 3 2 1 3 1 1 3 2 2 2 1
%e A353741 1 1 1 2 1 2 1 3 2 2 3 1 1 4 2 2 1 4 1 1 1 3 2
%e A353741 Row n = 7 counts the following partitions:
%e A353741 1111111 211111 31111 4111 511 61 7 421 331 52 43
%e A353741 22111 3211 2221 322
%t A353741 DeleteCases[Table[Length[Select[IntegerPartitions[n],Times@@#==k&]],{n,0,10},{k,1,2^n}],0,2]
%Y A353741 Row sums are A000041.
%Y A353741 Row lengths are A034891.
%Y A353741 A partial transpose is A319000.
%Y A353741 The full version with zeros is A339095, rank statistic A003963.
%Y A353741 A008284 counts partitions by sum, strict A116608.
%Y A353741 A225485 counts partitions by frequency depth.
%Y A353741 A266477 counts partitions by product of multiplicities, ranked by A005361.
%Y A353741 Cf. A002033, A266499, A325242, A325268, A325280, A353503, A353506, A353698.
%K A353741 nonn,tabf,less
%O A353741 0,11
%A A353741 _Gus Wiseman_, May 20 2022