MathDB

One moving point in the coordinate plane can move right or up one position.

N

is a number of all paths : paths that moving point starts from

(0, 0)

, without passing

(1, 0), (2, 1), . . . , (n, n-1)

and moves

2n

times to

(n, n)

a_k

is a number of special paths : paths include in

N

, but

k

th moves to the right,

k+1

th moves to the up. find

\frac{1}{N} (a_1+a_2+ . . . + a_{2n-1})

Problem Statement