The nth central fibonomial coefficient is defined as [2n n]_F | = | product_(k = 1)^n F_(n + k)/F_k | = | -(ϕ^(n^2) ((-1)^n ϕ^(-2 n) ; - ϕ^(-2))_(n + 1))/([(-1)^n ϕ^(-2 n) - 1](-ϕ^(-2) ; - ϕ^(-2))_n), where [n k]_F is a fibonomial coefficient, F_n is a Fibonacci number, ϕ is the golden ratio, and (a;q)_n is a q-Pochhammer symbol (E. W. Weisstein, Dec. 8, 2009). For n = 1, 2, ..., the first few are 1, 6, 60, 1820, 136136, ... (OEIS A003267).
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