KnowraExponential generating functionLinked fromLinked fromThe 8 pages that link to Exponential generating function, each with the reason it gives.All 8Broader topic 2Related 5Compared with 1Generating functionBroader topic: The factorial denominator makes this form especially suited to labeled combinatorial structures.FactorialRelated: Dividing coefficients by factorials makes labeled combinatorial structures combine neatly.Formal power seriesBroader topic: Its formal coefficients turn labelled constructions into useful algebraic operations.Dirichlet seriesCompared with: Factorial weights distinguish it from the reciprocal-power weights defining Dirichlet series.Stirling numbers of the second kindRelated: For fixed k, the exponential generating function is (eˣ−1)ᵏ/k!.Bell numberRelated: The Bell numbers have generating function exp(eˣ − 1), which yields useful identities.Lah numberRelated: The Lah numbers have a compact bivariate generating function encoding both indices.Twelvefold wayRelated: It naturally models assignments of distinguishable objects to labeled boxes.