Geodesic
On the generating function of discrete Chebyshev polynomials
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 124-134

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We give a closed form for the generating function of the discrete Chebyshev polynomials. The closed form consists of the MacWilliams transform of Jacobi polynomials together with a binomial multiplicative factor. It turns out that the desired closed form is a solution to a special case of the Heun differential equation, and that the closed form implies combinatorial identities that appear quite challenging to prove directly. 
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     author = {N. Gogin and M. Hirvensalo},
     title = {On the generating function of discrete {Chebyshev} polynomials},
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N. Gogin; M. Hirvensalo. On the generating function of discrete Chebyshev polynomials. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 124-134. http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a7/