Superfactorials

Neil Sloane and Simon Plouffe defined a superfactorial in The Encyclopedia of Integer Sequences (Academic Press, 1995) to be the product of the first factorials. So the superfactorial of 4 is

n\equiv 0(\mbox{mod k})

In general

n\equiv 0(\mbox{mod k})

Equivalently, the superfactorial is given by the formula

n\equiv 0(\mbox{mod k})

which is the determinant of a Vandermonde matrix.

The sequence of superfactorials starts (from n=0 )

A A A