Sum of squares of binomial coefficients

Given a positive integer n. The task is to find the sum of square of Binomial Coefficient i.e 
ⁿC₀² + ⁿC₁² + ⁿC₂² + ⁿC₃² + ......... + ⁿC_n-2² + ⁿC_n-1² + ⁿC_n² 
Examples: 

Input : n = 4
Output : 70

Input : n = 5
Output : 252

Method 1: (Brute Force) 
The idea is to generate all the terms of binomial coefficient and find the sum of square of each binomial coefficient.
Below is the implementation of this approach:

Output:  

70

Time Complexity: O(n²)
Space Complexity: O(n²)

Method 2: (Using Formula) 

= 
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Proof, 
 

We know,
(1 + x)n = nC0 + nC1 x + nC2 x2 + ......... + nCn-1 xn-1 + nCn-1 xn
Also,
(x + 1)n = nC0 xn + nC1 xn-1 + nC2 xn-2 + ......... + nCn-1 x + nCn

Multiplying above two equations,
(1 + x)2n = [nC0 + nC1 x + nC2 x2 + ......... + nCn-1 xn-1 + nCn-1 xn] X 
 [nC0 xn + nC1 xn-1 + nC2 xn-2 + ......... + nCn-1 x + nCn]

Equating coefficients of xn on both sides, we get
2nCn = nC02 + nC12 + nC22 + nC32 + ......... + nCn-22 + nCn-12 + nCn2

Hence, sum of the squares of coefficients = 2nCn = (2n)!/(n!)2.

Also, (2n)!/(n!)² = (2n * (2n - 1) * (2n - 2) * ..... * (n+1))/(n * (n - 1) * (n - 2) *..... * 1).
Below is the implementation of this approach: 
 

Output:  

70

Time Complexity: O(n)
Auxiliary Space: O(1)