Fibonacci coefficient

The fibonomial coefficient (sometimes also called simply the Fibonacci coefficient) is defined by [m k]_F = (F_m F_(m - 1) ...F_(m - k + 1))/(F_1 F_2 ...F_k), where [m 0]_F = 1 and F_n is a Fibonacci number. This coefficient satisfies [m n]_F = 1/2(L_n [m - 1 n]_F + L_(m - n) [m - 1 n - 1]_F) for k>0, where L_n is a Lucas number.

binomial coefficient | central fibonomial coefficient | Fibonacci number | fibonorial | Lucas number