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.
Triangle begins: 1; 1, 1; 1, 2, 1; 1, 4, 4, 1; 1, 7, 16, 7, 1; 1, 12, 53, 53, 12, 1; 1, 20, 166, 318, 166, 20, 1; 1, 33, 492, 1784, 1784, 492, 33, 1; 1, 54, 1413, 9288, 17840, 9288, 1413, 54, 1; 1, 88, 3960, 46233, 163504, 163504, 46233, 3960, 88, 1; 1, 143, 10912, 221859, 1418549, 2616064, 1418549, 221859, 10912, 143, 1;
T[n_, 1] := 1; T[n_, n_] := 1; T[n_, k_] := Fibonacci[(n - k + 1)]*T[ n - 1, k - 1] + Fibonacci[k ]*T[n - 1, k];
Table[T[n, m], {n, 1, 11}, {m, 1, n}] // Flatten (* Roger L. Bagula, Sep 09 2008 *)