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Let S(n)=""^(n)C(0)""^(n)C(1)+""^(n)C(1)...

Let `S_(n)=""^(n)C_(0)""^(n)C_(1)+""^(n)C_(1)""^(n)C_(2)+…..+""^(n)C_(n-1)""^(n)C_(n). "If" (S_(n+1))/(S_(n))=(15)/(4)`, find the sum of all possible values of `n (n in N)`

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