Here is one possible solution.

import math

def double_factorial(n):
    if not n % 2:
        # Even n: n!! = 2**(n/2).(n/2)!
        return 2**(n // 2) * math.factorial(n // 2)

    # Odd n: n!! = 1.3.5...(n-2)n
    dfactorial = 1
    for i in range(3, n+1, 2):
        dfactorial *= i
    return dfactorial


def sinm_cosn(m, n):
    """ Evaluate int_0^(pi/2) sin^m(x).cos^n(x) dx """

    fac = double_factorial(m-1) * double_factorial(n-1) / double_factorial(m+n)
    if m % 2 or n % 2:
        return fac
    return fac * math.pi / 2


for m in range(1,6):
    for n in range(1,6):
        print(n, m, sinm_cosn(m,n))