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 A212721 #23 Jun 29 2019 03:59:09
%S A212721 1,1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,6,1,2,3,4,5,6,8,9,1,2,3,4,5,6,7,8,9,
%T A212721 10,12,1,2,3,4,5,6,7,8,9,10,12,15,16,18,1,2,3,4,5,6,7,8,9,10,12,14,15,
%U A212721 16,18,20,24,27,1,2,3,4,5,6,7,8,9,10,12,14
%N A212721 Triangle read by rows: n-th row gives distinct products of partitions of n (A000041).
%C A212721 A034891(n) = length of n-th row;
%C A212721 A000792(n) = largest term of n-th row;
%C A212721 for n>5: A007918(n) = smallest number <= A000792(n) not occurring in n-th row.
%H A212721 Reinhard Zumkeller, <a href="/A212721/b212721.txt">Rows n = 0..36 of triangle, flattened</a>
%e A212721 A000041(6)=11, the 11 partitions and their products of 6:
%e A212721 1: (1,1,1,1,1,1) -> 1 * 1 * 1 * 1 * 1 * 1 = 1
%e A212721 2: (1,1,1,1,2) -> 1 * 1 * 1 * 1 * 2 = 2
%e A212721 3: (1,1,1,3) -> 1 * 1 * 1 * 3 = 3
%e A212721 4: (1,1,2,2) -> 1 * 1 * 2 * 2 = 4
%e A212721 5: (1,1,4) -> 1 * 1 * 4 = 4
%e A212721 6: (1,2,3) -> 1 * 2 * 3 = 6
%e A212721 7: (1,5) -> 1 * 5 = 5
%e A212721 8: (2,2,2) -> 2 * 2 * 2 = 8
%e A212721 9: (2,4) -> 2 * 4 = 8
%e A212721 10: (3,3) -> 3 * 3 = 9
%e A212721 11: (6) -> 6,
%e A212721 sorted and duplicates removed: T(6,1..8)=[1,2,3,4,5,6,8,9], A034891(6)=8.
%e A212721 The triangle begins:
%e A212721 0 | [1]
%e A212721 1 | [1]
%e A212721 2 | [1,2]
%e A212721 3 | [1,2,3]
%e A212721 4 | [1,2,3,4]
%e A212721 5 | [1,2,3,4,5,6]
%e A212721 6 | [1,2,3,4,5,6,8,9]
%e A212721 7 | [1,2,3,4,5,6,7,8,9,10,12]
%e A212721 8 | [1,2,3,4,5,6,7,8,9,10,12,15,16,18]
%e A212721 9 | [1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,24,27]
%e A212721 10 | [1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,25,27,30,32,36].
%t A212721 row[n_] := Union[Times @@@ IntegerPartitions[n]];
%t A212721 Table[row[n], {n, 0, 10}] (* _Jean-François Alcover_, Jun 29 2019 *)
%o A212721 (Haskell)
%o A212721 import Data.List (nub, sort)
%o A212721 a212721 n k = a212721_row n !! (k-1)
%o A212721 a212721_row = nub . sort . (map product) . ps 1 where
%o A212721 ps x 0 = [[]]
%o A212721 ps x y = [t:ts | t <- [x..y], ts <- ps t (y - t)]
%o A212721 a212721_tabf = map a212721_row [0..]
%o A212721 (Sage)
%o A212721 [sorted(list(set([mul(p) for p in Partitions(n)]))) for n in range(11)] # _Peter Luschny_, Dec 13 2015
%Y A212721 Cf. A000041, A000792, A034891.
%K A212721 nonn,tabf,look
%O A212721 0,4
%A A212721 _Reinhard Zumkeller_, Jun 14 2012