Question

Simplify
\[\huge \sum_{k=0}^n\frac{(2n!)}{(k!)^2((n-k)!)^2}\]

Answer 1

no calculating devices allowed eg wolfram

Answer 2

simplified form will be
C(2n,n) *summation ( C(n,k) )^2

rest is bit easier

Answer 3

is the question you asked also solving the same combinatrics

Answer 4

mine is an inequality question, its different from this

Answer 5

oh yeah thanks a lot