The first few values of product_(k = 1)^n k! (known as a superfactorial) for n = 1, 2, ... are given by 1, 2, 12, 288, 34560, 24883200, ... (OEIS A000178). The first few positive integers that can be written as a product of factorials are 1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, 72, ... (OEIS A001013). The number of ways that n! is a product of smaller factorials, each greater than 1, for n = 1, 2, ... is given by 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, ... (OEIS A034876), and the numbers of products of factorials not exceeding n! are 1, 2, 4, 8, 15, 28, 49, 83, ... (OEIS A101976).

factorial | factorial sums