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.
T(n,k) = [T(n,k+1),T(n,k+2),...,T(n,n)]*[T(k,k),T(k+1,k),...,T(n-1,k)]:
T(3,0) = [5,3,1]*[1,1,3] = 5*1 + 3*1 + 1*3 = 11;
T(4,1) = [7,4,1]*[1,2,5] = 7*1 + 4*2 + 1*5 = 20;
T(5,1) = [31,9,5,1]*[1,2,5,20] = 31*1 + 9*2 + 5*5 + 1*20 = 94;
T(6,2) = [44,11,6,1]*[1,3,7,31] = 44*1 + 11*3 + 6*7 + 1*31 = 150.
Triangle begins:
1;
1, 1;
3, 2, 1;
11, 5, 3, 1;
50, 20, 7, 4, 1;
257, 94, 31, 9, 5, 1;
1467, 507, 150, 44, 11, 6, 1;
9081, 3009, 853, 218, 59, 13, 7, 1;
60272, 19350, 5251, 1307, 298, 76, 15, 8, 1;
424514, 132920, 35109, 8313, 1881, 390, 95, 17, 9, 1;
3151226, 966962, 249332, 57738, 12315, 2587, 494, 116, 19, 10, 1;
24510411, 7396366, 1873214, 422948, 88737, 17377, 3437, 610, 139, 21, 11, 1;
...
{T(n,k)=if(n==k,1,if(n==k+1,n, sum(j=0,n-k-1,T(n,j+k+1)*T(j+k,k))))}
for(n=0,12,for(k=0,n, print1(T(n,k),", "));print(""))
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