prove the number of 2-by-n arrays [ x11 x12 ... x1n x21 x22 ... x2n ] that can be made from the numbers 1,2,...,2n such that x11 < x12 < ... < x1n x21 < x22 < ... < x2n x11 < x21, x12 < x22, ..., x1n < x2n equals the nth Catalan number, Cn