Is the largest coefficient in the expansion of binomial (a + b) ^ 2n odd or even, or not necessarily integer?

Is the largest coefficient in the expansion of binomial (a + b) ^ 2n odd or even, or not necessarily integer?


The expansion of (a + b) ^ (2n) has a total of 2n + 1 terms. The largest coefficient is the middle term, that is, the largest coefficient is C (n, 2n)