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Jozsef Wildt International Math Competition
2009 Jozsef Wildt International Math Competition
W. 30
Prove this combinatorial equation
Prove this combinatorial equation
Source: 2009 Jozsef Wildt International Math Competition
April 27, 2020
combinatorics
Problem Statement
Prove that
∑
0
≤
i
<
j
≤
n
(
i
+
j
)
(
n
i
)
(
n
j
)
=
n
(
2
2
n
−
1
−
(
2
n
−
1
n
)
)
\sum \limits_{0\leq i<j\leq n}(i+j) {{n}\choose{i}}{{n}\choose{j}}=n\left (2^{2n-1}-{{2n-1}\choose{n}} \right )
0
≤
i
<
j
≤
n
∑
(
i
+
j
)
(
i
n
)
(
j
n
)
=
n
(
2
2
n
−
1
−
(
n
2
n
−
1
)
)
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