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