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] (because is 10)
Values
The first few terms for the sequence \(\mathrm{expostfacto}(n)\) are shown below:
\begin{eqnarray} \mathrm{expostfacto}(1) &=& 1 \\ \mathrm{expostfacto}(2) &=& 2 \\ \mathrm{expostfacto}(3) &=& 9 \\ \mathrm{expostfacto}(4) &=& 4^{362880} \approx 3.38573599\times10^{218475} \\ \mathrm{expostfacto}(5) &=& 5^{(4^{362880})!} \approx 10^{10^{7.39698994\times10^{218480}}} \\ \end{eqnarray}
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