The superfactorial of n is defined by Pickover (1995) as
n$=n!^(n!^(·^(·^(·^(n!)))))_()_(n!).
(1)
The first two values are 1 and 4, but subsequently grow so rapidly that 3$ already has a huge number of digits.
Superfactorial
Sloane and Plouffe (1995) define the superfactorial by
n$=product_(k=1)^(n)k!
(2)
=G(n+2),
(3)
which is equivalent to the integral values of the Barnes G-function. The values for n=1, 2, ... are 1, 1, 2, 12, 288, 34560, ... (OEIS A000178). This function has an unexpected connection with Bell numbers. |