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 A323848 #30 Feb 10 2019 08:46:25 %S A323848 0,4,18,25,68,386,256,250,4657,12200,4356,922,54219,432842,608993, %T A323848 123904,3430,642815,14697256,60650883,49489706,5909761,12868,7852836, %U A323848 514608568,5713126349,13458882036,6648891794,473497600,48618,98755951,18971384148,558848240787,3406380649146,4857082197177,1489334202216,63799687396 %N A323848 Irregular triangle read by rows: T(n,d) (n >= 1, d <= n-1 for n>1) = number of n X n integer-valued matrices M such that M_{1,1}=0, M_{n,n}=d, M_{(i+1),j} = M_{i,j} + (0 or 1), M_{i,(j+1)} = M_{i,j} + (0 or 1), and M_{(i+1),(j+1)} = M_{i,j} + (0 or 1). %C A323848 T(n,n-1) = A005157(n-1)^2 for n >= 2. See Knuth (2019) link. %D A323848 D. E. Knuth, Email to N. J. A. Sloane, Feb 06 2019. %H A323848 Alois P. Heinz, <a href="/A323848/b323848.txt">Rows n = 1..14, flattened</a> %H A323848 Don Knuth, <a href="https://cs.stanford.edu/~knuth/papers/noncr-conj.pdf">A conjecture about noncrossing paths</a>, Feb 06 2019. %F A323848 T(n,1) = binomial(2n,n) - 2. %e A323848 Triangle begins: %e A323848 n\d 1 2 3 4 5 6 7 %e A323848 1 0 0 0 0 0 0 0 %e A323848 2 4 0 0 0 0 0 0 %e A323848 3 18 25 0 0 0 0 0 %e A323848 4 68 386 256 0 0 0 0 %e A323848 5 250 4657 12200 4356 0 0 0 %e A323848 6 922 54219 432842 608993 123904 0 0 %e A323848 7 3430 642815 14697256 60650883 49489706 5909761 0 %e A323848 ... %Y A323848 Columns d=1-2 give: A115112, A306322. %Y A323848 Cf. A005157, A323849. %K A323848 nonn,tabf %O A323848 1,2 %A A323848 _N. J. A. Sloane_, Feb 07 2019 %E A323848 More terms from _Alois P. Heinz_, Feb 07 2019