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The Exporian is a function invented by Aalbert Torsius.[1] It is defined as \(ExT(x) = x!x!x = x!!3\), using Torsius' definition of the expofactorial:

\(x!x!n = \prod^{x}_{i = 1} i!(n - 1) = 1!(n - 1) \cdot 2!(n - 1) \cdot \ldots \cdot x!(n - 1)\),

\(x!x!0 = x\)

This definition is a generalization of the ordinary factorial: \(x!x!1 = x!x!\).

Pseudocode Edit

// Torsius' expofactorial extension
function expofactorialTorsius(z, x):
    if x = 0:
        return z
    result := 1
    for i from 1 to z:
        result := result * expofactorialTorsius(i, x - 1)
    return result

// Exporian
function exporian(x):
    return expofactorialTorsius(x, x)

Sources Edit

  1. [1]
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