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1982 IMO Longlists
49
Simplify the sum (2n)! / (k! (n-k)!)^2
Simplify the sum (2n)! / (k! (n-k)!)^2
Source: IMO LongList 1982 - P49
May 16, 2011
number theory proposed
number theory
Problem Statement
Simplify
∑
k
=
0
n
(
2
n
)
!
(
k
!
)
2
(
(
n
−
k
)
!
)
2
.
\sum_{k=0}^n \frac{(2n)!}{(k!)^2((n-k)!)^2}.
k
=
0
∑
n
(
k
!
)
2
((
n
−
k
)!
)
2
(
2
n
)!
.
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