Expostfacto function

The expostfacto function is a function invented by Tom Kreitzberg defined as $$\mathrm{expostfacto}(n) = n^{\mathrm{expostfacto}(n-1)!}$$, where $$\mathrm{expostfacto}(1) = 1$$. The first few terms for the sequence $$\mathrm{expostfacto}(n)$$ where n = 1, 2, 3, etc., are 1, 2, 9, and $$4^{362880}$$.