| Expostfacto function | |
|---|---|
| Notation | \(\mathrm{expostfacto}(n)\) |
| Type | Combinatorial |
| Based on | Factorial |
| Growth rate | \(f_{3}(n)\) |
| Author | Tom Kreitzberg |
The expostfacto function is a function invented by Tom Kreitzberg defined as \(\mathrm{expostfacto}(n) = n^{\mathrm{expostfacto}(n-1)!}\), where \(\mathrm{expostfacto}(1) = 1\).[1]
Values[]
The first few terms for the sequence \(\mathrm{expostfacto}(n)\) are shown below:
\begin{eqnarray} \mathrm{expostfacto}(1) &=& 1 \\ \mathrm{expostfacto}(2) &=& 2^{1} = 2 \\ \mathrm{expostfacto}(3) &=& 3^{2} = 9 \\ \mathrm{expostfacto}(4) &=& 4^{362,880} \approx 3.38573599\times10^{218,475} \\ \mathrm{expostfacto}(5) &=& 5^{(4^{362,880})!} \approx 10^{10^{7.39698994\times10^{218,480}}} \\ \end{eqnarray}
Expostfacto function grows as fast as \(f_3(f_1(n))\) in the fast-growing hierarchy.
Sources[]
See also[]
Main article: Factorial
Multifactorials: Double factorial · MultifactorialFalling and rising: Falling factorial · Rising factorial
Other mathematical variants: Alternating factorial · Hyperfactorial · q-factorial · Roman factorial · Subfactorial · Weak factorial · Primorial · Compositorial · Semiprimorial
Tetrational growth: Exponential factorial · Expostfacto function · Superfactorial by Clifford Pickover
Nested Factorials: Tetorial · Petorial · Ectorial · Zettorial · Yottorial
Array-based extensions: Hyperfactorial array notation · Nested factorial notation
Other googological variants: · Tetrofactorial · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial · Bouncing Factorial