ProjectEuler#15 Lattice paths

#Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly #6 routes to the bottom right corner.

#How many such routes are there through a 20×20 grid?

n = 20
array = []

for i in range(n+1):
    array.append([])

#only one way to get to each of these points(first row), so we mark each of those with a 1
for x in range(0,n+1):
    array[0].append(1)

#only one way to get to each of these points(first col), so we mark each of those with a 1
for y in range(1,n+1):
    array[y].append(1)

#starting at element element (1,1) we add above element mark and left element mark.
for x in range(1,n+1):
    for y in range(1,n+1):
        array[x].append(array[x][y-1]+array[x-1][y])

print array[20][20]