User blog:GamesFan2000/Arrayfactorials

An arrayfactorial is the product of every possible array built with n entries or less and with n or less-valued entries(no arrays within the arrays unless specified in n).

0! = 1

1! = {1} = 1

2! = {2, 2} * {2, 1} * {2} = 16

3! = {3, 3, 3} * {3, 3, 2} * {3, 3, 1} * {3, 2, 3} * {3, 1, 3} * {2, 3, 3} * {3, 2, 2} * {3, 2, 1} * {3, 1, 2} * {3, 1, 1} * {2, 3, 2} * {2, 3, 1} * {2, 2, 3} * {2, 1, 3} * {2, 2, 2} * {2, 2, 1} * {2, 1, 2} * {2, 1, 1} * {3, 3} * {3, 2} * {3, 1} * {2, 3} * {2, 2} * {2, 1} * {3} * {2} = (3^^^3)*(3^^3)*(3^3)*(3^^^2)*(3)*(2^^^3)*(3^^2)*(3^2)*(3)*(3)*(2^^3)*(2^3)*(2^^^2)*(2)*(2^^2)*(2^2)*(2)*(2)*(27)*(9)*(3)*(8)*(4)*(2)*(3)*(2)