Question 91
For a given natural number $n$ specify the number of paths of length $2n + 2$ from point $[0, 0]$ to the point $[n, n]$ which do not pass any point more than once. Path of length $2n + 2$ connecting points $[0, 0]$ and $[n, n]$ means $(2n + 2)$-tuple
$$
(A_0A_1, A_1A_2, A_2A_3, \dots, A_{2n+1}A_{2n+2})
$$
of line segments connecting two adjacent lattice points, while $A_0 = [0, 0]$, $A_{2n+2} = [n, n]$. (Pavel Novotný)
$$
(A_0A_1, A_1A_2, A_2A_3, \dots, A_{2n+1}A_{2n+2})
$$
of line segments connecting two adjacent lattice points, while $A_0 = [0, 0]$, $A_{2n+2} = [n, n]$. (Pavel Novotný)