problems = {n^3 + 1, (n + 1)/(n - 1), Binomial[2 n, n], Fibonacci[n], (n/2)! Exp[n], (n/2) + Exp[n], (n/5)!, ( Pochhammer[Subscript[a, 1], n] Pochhammer[Subscript[a, 2], 2 n + 1])/Pochhammer[Subscript[b, 1], n], ChebyshevT[2 n, 1] Pochhammer[Subscript[a, 1], n]};
FormulaGallery[forms_List] := Module[{vals = ParallelMap[DifferenceRootReduce[#, n] &, forms]}, Text@TraditionalForm@ Grid[Table[{forms[[i]], First@vals[[i]][[0, 1]][y, n]}, {i, Length[forms]}], Dividers -> All, Alignment -> {Left, Baseline}, Background -> LightYellow, Spacings -> {1, 2}]]
FormulaGallery[problems]