  This paper introduces a new generalized superfactorial function (referable to
as $n^{th}$- degree superfactorial: $sf^{(n)}(x)$) and a generalized
hyperfactorial function (referable to as $n^{th}$- degree hyperfactorial:
$H^{(n)}(x)$), and we show that these functions possess explicit formulae
involving figurate numbers. Besides discussing additional number patterns, we
also introduce a generalized primorial function and 2 related theorems. Note
that the superfactorial definition offered by Sloane and Plouffe (1995) is the
definition considered (and not Clifford Pickover's (1995) superfactorial
function: $n\$$).
