Expostfacto function
Notation\(\mathrm{expostfacto}(n)\)
TypeCombinatorial
Based onFactorial
Growth rate\(f_{3}(n)\)
AuthorTom 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 · Multifactorial
Falling 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
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