It's a combinatorial problem which is disturbing me from couple of days now. I was going through Catalan Numbers here
There is a property of a catalan number that
Cn is the number of monotonic lattice paths along the edges of a grid with n × n square cells, which do not pass above the diagonal
Lets take example For N = 3, the monotonic lattice paths are [0 0 0 3], [0 0 1 2], [0 0 2 1], [0 1 0 2], [0 1 1 1]. (Note : The notation used here is the increase in column-height.)
I need to have count of 1's in all of these paths. So, Total no of 1's = 6.
How do I approach this problem? I have very less knowledge of combinatorics.