Valid Dates

import math
import itertools

num_pairs = int(input("Enter Number of Pairs of Brothers and Sisters: "))

# calculates total number of valid pairings and prints them all
def calculate_total_va(n):
    # creates arrays containing all possible sister permutation
    sisters = []
    for i in range (1, n + 1):
        sisters.append("x" + str(i))
        sisters.append("y" + str(i))
    sisters = itertools.permutations(sisters)
    
    # calculates total number of valid pairings and prints each one
    count = 0
    for permutation in sisters:
        isValid = True
        for i in range(0, n * 2, 2):
            if (int(permutation[i][1]) == int(permutation[i + 1][1])):
                isValid = False
        if isValid:
            count += 1
            print(permutation)
    print("Valid Pairs: " + str(count))

def calculate_total_vb(n):
    # creates an array that stores R(n)
    recurrence_r = [0, 0]
    for k in range(2, n + 1):
        recurrence_r.append(2 ** (2 * k - 1) * math.factorial(k) * math.factorial(k - 1))

    # creates an array that stores T(n)
    recurrence_t = [1] + [0] * n 
    for i in range(1, n + 1):
        total = 0
        for k in range(2, i + 1):
            total += (recurrence_r[k] * recurrence_t[i - k] * math.comb(i, k) * math.comb(i - 1, k - 1))
        recurrence_t[i] = total
        print("T(" + str(i) + "):\t" + str(recurrence_t[i]))

# calculates total number of valid pairings
def calculate_total_vc(n):
    # creates an array that stores T(n)
    recurrence_t = [1] + [0] * n
    for i in range(2, n + 1):
        recurrence_t[i] = 2 * i * 2 * (i - 1) * (recurrence_t[i - 2] * 2 * (i - 1) + recurrence_t[i - 1])
        print("T(" + str(i) + "):\t" + str(recurrence_t[i]))

# prints results
print("Part A")
calculate_total_va(num_pairs)
print("Part B")
calculate_total_vb(num_pairs)
print("Part C")
calculate_total_vc(num_pairs)