A generating function is a formal power series whose coefficients correspond to the terms of a sequence, often used to encode information about combinatorial structures. By expressing sequences as coefficients in a power series, generating functions provide a powerful tool for solving counting problems, manipulating sequences, and deriving relationships between different combinatorial objects. They can be particularly useful in representing complex combinatorial structures such as Lah numbers and partitions.
congrats on reading the definition of Generating Function. now let's actually learn it.