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Prove that (C0+C1)(C1+C2)(C2+C3)(C3+...

Prove that
`(C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n)` = `(C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)`

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