Number of triangular 0..1 arrays with n rows such that the k-th row of the array (with the first row of the triangle indexed with 0) has 2*k+1 elements and row sums are nondecreasing from top to bottom.

A256369

Number of triangular 0..1 arrays with n rows such that the k-th row of the array (with the first row of the triangle indexed with 0) has 2*k+1 elements and row sums are nondecreasing from top to bottom.