A formal (or analytic) series Σ a_n x^n or Σ a_n x^n/n! encoding a combinatorial sequence. Algebraic operations on series mirror combinatorial constructions (sum, product, composition).
Generating function
Related concepts
- Power series
- Exponential generating function
- Cayley's formula
- Linear recurrence a_{n+k} + c_{k-1}a_{n+k-1} + ... = 0: characteristic-poly solution
- Z-transform X(z) = Σ_n x[n] z^{-n}: discrete-time analogue of Laplace
- Partition function
- N-glycan antennarity: (1+x)^n GF; tri-core subsets = 2³ = 8; binomial(n,k) antennary structures