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 A138121 #64 May 12 2020 10:57:17
%S A138121 1,2,1,3,1,1,4,2,2,1,1,1,5,3,2,1,1,1,1,1,6,3,3,4,2,2,2,2,1,1,1,1,1,1,
%T A138121 1,7,4,3,5,2,3,2,2,1,1,1,1,1,1,1,1,1,1,1,8,4,4,5,3,6,2,3,3,2,4,2,2,2,
%U A138121 2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,9,5,4,6,3,3,3,3,7,2,4,3,2,5,2,2,3,2,2
%N A138121 Triangle read by rows in which row n lists the partitions of n that do not contain 1 as a part in juxtaposed reverse-lexicographical order followed by A000041(n-1) 1's.
%C A138121 Mirror of triangle A135010.
%H A138121 Robert Price, <a href="/A138121/b138121.txt">Table of n, a(n) for n = 1..16851, 25 rows</a>
%H A138121 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpatru.jpg">A section model of partitions (2D and 3D)</a> [From _Omar E. Pol_, Sep 07 2008]
%H A138121 Robert Price, <a href="/A138121/a138121.txt">Mathematica Program to Generate Diagram</a>
%e A138121 Triangle begins:
%e A138121 [1];
%e A138121 [2],[1];
%e A138121 [3],[1],[1];
%e A138121 [4],[2,2],[1],[1],[1];
%e A138121 [5],[3,2],[1],[1],[1],[1],[1];
%e A138121 [6],[3,3],[4,2],[2,2,2],[1],[1],[1],[1],[1],[1],[1];
%e A138121 [7],[4,3],[5,2],[3,2,2],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1];
%e A138121 ...
%e A138121 The illustration of the three views of the section model of partitions (version "tree" with seven sections) shows the connection between several sequences.
%e A138121 ---------------------------------------------------------
%e A138121 Partitions A194805 Table 1.0
%e A138121 . of 7 p(n) A194551 A135010
%e A138121 ---------------------------------------------------------
%e A138121 7 15 7 7 . . . . . .
%e A138121 4+3 4 4 . . . 3 . .
%e A138121 5+2 5 5 . . . . 2 .
%e A138121 3+2+2 3 3 . . 2 . 2 .
%e A138121 6+1 11 6 1 6 . . . . . 1
%e A138121 3+3+1 3 1 3 . . 3 . . 1
%e A138121 4+2+1 4 1 4 . . . 2 . 1
%e A138121 2+2+2+1 2 1 2 . 2 . 2 . 1
%e A138121 5+1+1 7 1 5 5 . . . . 1 1
%e A138121 3+2+1+1 1 3 3 . . 2 . 1 1
%e A138121 4+1+1+1 5 4 1 4 . . . 1 1 1
%e A138121 2+2+1+1+1 2 1 2 . 2 . 1 1 1
%e A138121 3+1+1+1+1 3 1 3 3 . . 1 1 1 1
%e A138121 2+1+1+1+1+1 2 2 1 2 . 1 1 1 1 1
%e A138121 1+1+1+1+1+1+1 1 1 1 1 1 1 1 1 1
%e A138121 . 1 ---------------
%e A138121 . *<------- A000041 -------> 1 1 2 3 5 7 11
%e A138121 . A182712 -------> 1 0 2 1 4 3
%e A138121 . A182713 -------> 1 0 1 2 2
%e A138121 . A182714 -------> 1 0 1 1
%e A138121 . 1 0 1
%e A138121 . A141285 A182703 1 0
%e A138121 . A182730 A182731 1
%e A138121 ---------------------------------------------------------
%e A138121 . A138137 --> 1 2 3 6 9 15..
%e A138121 ---------------------------------------------------------
%e A138121 . A182746 <--- 4 . 2 1 0 1 2 . 4 ---> A182747
%e A138121 ---------------------------------------------------------
%e A138121 .
%e A138121 . A182732 <--- 6 3 4 2 1 3 5 4 7 ---> A182733
%e A138121 . . . . . 1 . . . .
%e A138121 . . . . 2 1 . . . .
%e A138121 . . 3 . . 1 2 . . .
%e A138121 . Table 2.0 . . 2 2 1 . . 3 . Table 2.1
%e A138121 . . . . . 1 2 2 . .
%e A138121 . 1 . . . .
%e A138121 .
%e A138121 . A182982 A182742 A194803 A182983 A182743
%e A138121 . A182992 A182994 A194804 A182993 A182995
%e A138121 ---------------------------------------------------------
%e A138121 .
%e A138121 From _Omar E. Pol_, Sep 03 2013: (Start)
%e A138121 Illustration of initial terms (n = 1..6). The table shows the six sections of the set of partitions of 6. Note that before the dissection the set of partitions was in the ordering mentioned in A026792. More generally, the six sections of the set of partitions of 6 also can be interpreted as the first six sections of the set of partitions of any integer >= 6.
%e A138121 Illustration of initial terms:
%e A138121 ---------------------------------------
%e A138121 n j Diagram Parts
%e A138121 ---------------------------------------
%e A138121 . _
%e A138121 1 1 |_| 1;
%e A138121 . _ _
%e A138121 2 1 |_ | 2,
%e A138121 2 2 |_| . 1;
%e A138121 . _ _ _
%e A138121 3 1 |_ _ | 3,
%e A138121 3 2 | | . 1,
%e A138121 3 3 |_| . . 1;
%e A138121 . _ _ _ _
%e A138121 4 1 |_ _ | 4,
%e A138121 4 2 |_ _|_ | 2, 2,
%e A138121 4 3 | | . 1,
%e A138121 4 4 | | . . 1,
%e A138121 4 5 |_| . . . 1;
%e A138121 . _ _ _ _ _
%e A138121 5 1 |_ _ _ | 5,
%e A138121 5 2 |_ _ _|_ | 3, 2,
%e A138121 5 3 | | . 1,
%e A138121 5 4 | | . . 1,
%e A138121 5 5 | | . . 1,
%e A138121 5 6 | | . . . 1,
%e A138121 5 7 |_| . . . . 1;
%e A138121 . _ _ _ _ _ _
%e A138121 6 1 |_ _ _ | 6,
%e A138121 6 2 |_ _ _|_ | 3, 3,
%e A138121 6 3 |_ _ | | 4, 2,
%e A138121 6 4 |_ _|_ _|_ | 2, 2, 2,
%e A138121 6 5 | | . 1,
%e A138121 6 6 | | . . 1,
%e A138121 6 7 | | . . 1,
%e A138121 6 8 | | . . . 1,
%e A138121 6 9 | | . . . 1,
%e A138121 6 10 | | . . . . 1,
%e A138121 6 11 |_| . . . . . 1;
%e A138121 ...
%e A138121 (End)
%t A138121 less[run1_, run2_] := (lg1 = run1 // Length; lg2 = run2 // Length; lg = Max[lg1, lg2]; r1 = If[lg1 == lg, run1, PadRight[run1, lg, 0]]; r2 = If[lg2 == lg, run2, PadRight[run2, lg, 0]]; Order[r1, r2] != -1); row[n_] := Join[Array[1 &, {PartitionsP[n - 1]}], Sort[Reverse /@ Select[IntegerPartitions[n], FreeQ[#, 1] &], less]] // Flatten // Reverse; Table[row[n], {n, 1, 9}] // Flatten (* _Jean-François Alcover_, Jan 15 2013 *)
%t A138121 Table[Reverse/@Reverse@DeleteCases[Sort@PadRight[Reverse/@Cases[IntegerPartitions[n], x_ /; Last[x]!=1]], x_ /; x==0, 2]~Join~ConstantArray[{1}, PartitionsP[n - 1]], {n, 1, 9}] // Flatten (* _Robert Price_, May 11 2020 *)
%Y A138121 Row n has length A138137(n).
%Y A138121 Rows sums give A138879.
%Y A138121 Cf. A000041, A135010, A138879, A138880, A141285, A182703, A194812, A206437, A211009.
%K A138121 nonn,tabf,less
%O A138121 1,2
%A A138121 _Omar E. Pol_, Mar 21 2008