WFL of course meant "combinatorial proof" :^) * Victor Miller <victorsmiller@gmail.com> [Jul 04. 2013 07:38]:
Proof: f(x) := 1/sqrt(1-4*x) = sum_{n=0}^{\infty} \binom{2n}{n} x^n. Your sum is the coefficient of x^n in f(x)^2, i.e. the coefficient of x^n in 1/(1-4*x), which is 4^n.
Victor
On Wed, Jul 3, 2013 at 11:12 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Prove sum_(j = 0)^(j = n) (2j)_C_j (2n-2j)_C_(n-j) = 4^n
eg. with n = 4 , 1.20 + 2.6 + 6.2 + 20.1 = 64
Fred Lunnon
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