## FANDOM

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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 Edit

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^{362880} \approx 3.38573599\times10^{218475} \\ \mathrm{expostfacto}(5) &=& 5^{(4^{362880})!} \approx 10^{10^{7.39698994\times10^{218480}}} \\ \end{eqnarray}

Expostfacto function grows as fast as $$f_3(f_1(n))$$ in the fast-growing hierarchy.

### Sources Edit

1. Really Big Numbers