# How to simplify Binomial expressions?

Binomial[2 n, 2 a]/Binomial[n, a]^2


I come across this expression, but no simplification command is working.
Can it be simplified further?

• – george2079 Nov 17 '16 at 22:05
• @george2079 Thanks a lot for the very useful link. It helped up to some point, may not be completely. But was great. – Shamina Nov 18 '16 at 9:51

Binomial[2 n,n] / (Binomial[2 a, a] Binomial[2(n-a), n-a])

which may, depending on your problem, provide some further insights. But I think your form or mine hit the limit of what one would consider "simplifying" unless $n$ and/or $a$ are known.
Note that $$(2n)! = n! 2^n (2n-1)!!,$$ so one can cancel out one pair of factorials in $$\binom{2n}n = 2^n\frac{(2n-1)!!}{n!},$$ if they really want. Normally this would not be called a simplification but I've seen many problems where it lead to one. This could be applied up to three times in the other expression – again, depending on what you want to achieve.