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.
The top left corner of the array:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, ...
2, 5, 0, 4, 3, 1, 8, 11, 6, 10, 9, 7, 14, ...
3, 4, 1, 5, 2, 0, 9, 10, 7, 11, 8, 6, 15, ...
4, 3, 5, 1, 0, 2, 10, 9, 11, 7, 6, 8, 16, ...
5, 2, 4, 0, 1, 3, 11, 8, 10, 6, 7, 9, 17, ...
6, 7, 14, 15, 22, 23, 0, 1, 12, 13, 18, 19, 8, ...
7, 6, 15, 14, 23, 22, 1, 0, 13, 12, 19, 18, 9, ...
8, 11, 12, 16, 21, 19, 2, 5, 14, 17, 20, 23, 6, ...
9, 10, 13, 17, 20, 18, 3, 4, 15, 16, 21, 22, 7, ...
10, 9, 17, 13, 18, 20, 4, 3, 16, 15, 22, 21, 11, ...
11, 8, 16, 12, 19, 21, 5, 2, 17, 14, 23, 20, 10, ...
12, 19, 8, 21, 16, 11, 14, 23, 2, 20, 17, 5, 0, ...
...
For A(1,2) (row=1, column=2, both starting from zero), we take as permutation p the permutation which has rank=1 in the ordering used by A060118, which is a simple transposition (1 2), which we can extend with fixed terms as far as we wish (e.g., like {2,1,3,4,5,...}), and as permutation q we take the permutation which has rank=2 (in the same list), which is {1,3,2}. We compose these from the left, so that the latter one, q, acts first, thus c(i) = p(q(i)), and the result is permutation {2,3,1}, which is listed as the 3rd one in A060118, thus A(1,2) = 3.
For A(2,1) we compose those two permutations in opposite order, as d(i) = q(p(i)), which gives permutation {3,1,2} which is listed as the 5th one in A060118, thus A(2,1) = 5.
...... Triangle............................ Row sums ........1........................................1 .......10.......0...............................10 ......115......10...0..........................125 = 5^3 .....1666.....139...0....0....................1805 = 5*19^2 ....30198....2570...0....0...0...............32768 = 32^3 = 8^5 ...665148...47878...904..0...0...0..........713930 .17296851.1017174.20972..0...0...0...0....18334997 T(1,1)=1, as there is just one non-identity, non-recursive Catalan bijection with a single non-default clause opening a single node, namely A089840[1]=A069770. T(2,1)=10, as there are the following non-recursive Catalan bijections (rows 2-11 of A089840): A072796, A089850, A089851, A089852, A089853, A089854, A072797, A089855, A089856, A089857, whose minimum clause-representation consists of a single non-default clause that opens two nodes. T(3,2)=10, as there are the following non-recursive Catalan bijections (rows 12-21 of A089840): A074679, A089858, A073269, A089859, A089860, A074680, A089861, A073270, A089862, A089863, whose minimum clause-representation consists of a two non-default clauses with total 3 nodes opened.
When A089840[1] = A069770 (swap binary tree sides) is applied to the left subtree of a binary tree, we get A089840[7] = A089854, thus a(1)=7. When A089840[12] = A074679 is applied to the left subtree of a binary tree, we get A089840[4207] = A089865, thus a(12)=4207.
When A089840(1) = A069770 (swap binary tree sides) is applied to the right subtree of a binary tree, we get A089850 = A089840(3), thus a(1)=3. When A089840(12) = A074679 is applied to the right subtree of a binary tree, we get A154121 = A089840(3655), thus a(12)=3655.
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