For positive integer n, the K-function is defined by K(n) | congruent | 1^1 2^2 3^3 ...(n - 1)^(n - 1) | = | H(n - 1), where the numbers H(n) = K(n + 1) are called hyperfactorials by Sloane and Plouffe. It is related to the Barnes G-function by K(n) = [Γ(n)]^(n - 1)/(G(n)). The first few values of K(n) for n = 1, 2, ... are 1, 1, 4, 108, 27648, 86400000, 4031078400000, ... (OEIS A002109).

Barnes G-function | Glaisher-Kinkelin constant | hyperfactorial