FindGeneratingFunction

FindGeneratingFunction[{a0,a1,…},x] attempts to find a simple generating function in x whose nth series coefficient is an.

FindGeneratingFunction[{{n0,a0},{n1,a1},…},x] attempts to find a simple generating function whose nith series coefficient is ai.

Examples

(* Find generating function for Fibonacci numbers *)
FindGeneratingFunction[{1, 1, 2, 3, 5, 8, 13}, x]

(* Find generating function for factorial *)
FindGeneratingFunction[{1, 1, 2, 6, 24, 120}, x]

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