A053199 Triangular array T: put T(n,0)=n+1 for all n >= 0 and all other T(n,k)=0; then put T(n,k)=Sum{T(i,j): 0<=j<=i-n+k, n-k<=i<=n}.
1, 2, 3, 3, 5, 14, 4, 7, 21, 60, 5, 9, 28, 84, 246, 6, 11, 35, 108, 328, 980, 7, 13, 42, 132, 410, 1260, 3824, 8, 15, 49, 156, 492, 1540, 4780, 14688, 9, 17, 56, 180, 574, 1820, 5736, 17952, 55720, 10, 19, 63, 204, 656, 2100, 6692
Offset: 0
Examples
Rows: {1}, {2,3}, {3,5,14}, {4,7,21,60}, ...