Write down an expression for the number of binomial paths which cross a rectangle from the point (0,0) to the point (3n,2m), with n,m 1, but which are constrained to have a vertex on the point (n,m)?

Question

Write down an expression for the number of binomial paths which cross a rectangle from the point (0,0) to the point (3n,2m), with n,m > 1, but which are constrained to have a vertex on the point (n,m)?