This is a list of factorial and binomial topics in mathematics. They are completely randomized design, randomized block design, and factorial designs. For any integer "n", the factorial "n"! Primes of the form are called factorial primes. This shows why the factorial of a half-integer is a rational multiple of formula 40. Interactions are often considered in the context of regression analyses or factorial experiments. For nonparametric alternatives in the factorial layout, see Sawilowsky. Since , 9 is an exponential factorial. Montgomery gives the following example of a fractional factorial experiment. The denominators of "S" divide the factorial . The second one is based on analytic bounds for the factorial function. The notation used to denote factorial experiments conveys a lot of information. An alternate notation for the rising factorial is the less common . Equilines of amplitude and phase of factorial are shown in figure. For the vast majority of factorial experiments, each factor has only two levels.