The analogues of some binomial coefficients

The unique positive zero of F-m (u) := u(2m) - u(m + 1) - u(m - 1) - 1 leads to analogues of 2 (2n k) (k even) by using hypergeometric functions. We show that their minimal polynomials are related to Chebyshev polynomials. Finally, we see how to compute the minimal polynomial of an analogue of 2 (2n k) (k > 2) by using an analogue of 2 (2n 2).