Question

Prove that $\sum_{l=0}^{n} \binom{n}{l}^2 (x+y)^{2l} (x-y)^{2(n-l)} = \sum_{l=0}^{n} \binom{2l}{l} \binom{2(n-l)}{n-l} x^{2l}y^{2(n-l)}$

score 805 · Answer 1 · 2017-10-15 06:06:06

Prove that $\sum_{l=0}^{n} \binom{n}{l}^2 (x+y)^{2l} (x-y)^{2(n-l)} = \sum_{l=0}^{n} \binom{2l}{l} \binom{2(n-l)}{n-l} x^{2l}y^{2(n-l)}$

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248

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List Question

Prove that $\sum_{l=0}^{n} \binom{n}{l}^2 (x+y)^{2l} (x-y)^{2(n-l)} = \sum_{l=0}^{n} \binom{2l}{l} \binom{2(n-l)}{n-l} x^{2l}y^{2(n-l)}$

A Chess Tournament : All Time Same Number of Game Player

Prove the set partition identity via double counting argument

Is there a combinatorial interpretation of the triangular numbers?

Combinatorical method proving Euler's theorem

Combinatorial proof that central binomial coefficients are the largest ones

Prove this conjecture for $k = 4$ i.e. prove that whatever moves $A$ can come up with, $B$ can always reply such that, in the end, $A$ has no moves.

count pairs of non-crossing partitions that differ by one transposition

Prove Eulerian Number using Combinatorics.

Number of ordered set partitions with subset size $\leq 3$

Combinatorics : relationship between Combinations and Permutations with similar objects

combinational proof for $\binom{n}{k}=\frac{n}{k}*\binom{n-1}{k-1}$ (not algebraic) Understanding the order that cause division.

Eulerian Polynomial Generating Function Proof

Number of ways to select $k$ books from a shelf with $n$ books so that no two adjacent books are selected

Give a direct a expression for the terms of the square of an infinite series

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