import numpy as np
import fractions as fr

N = 4
arr = np.empty((N * 2 + 1, N * 2 + 1, 2), dtype='object')

def plus(i, j):
    arr[i + 1, j] = 4 * arr[i, j] - arr[i - 1, j] - arr[i, j + 1] - arr[i, abs(j - 1)]

def even(i):
    arr[i, i] = arr[i - 1, i - 1] + [0, fr.Fraction(2, 2 * i - 1)]
    for k in range(1, i + 1): plus(i + k - 1, i - k)

def odd(i):
    arr[i + 1, i] = 2 * arr[i, i] - arr[i, i - 1]
    for k in range(1, i + 1): plus(i + k, i - k)

arr[0, 0] = 0
arr[1, 0] = [fr.Fraction(1, 2), 0]

for i in range(1, N):
    even(i)
    odd(i)

even(N)

for i in range(0, N + 1):
    for j in range(0, N + 1):
        a, b = arr[max(i, j), min(i, j)]
        print('(', a, ')+(', b, ')/π', sep='', end='t')
    print()