Is there any approximation formula for this equation? I have been trying to find approximations for it so I can create an approximation formula myself for something else, but for some reason I can't find any approximations online for this function although its simplicity. I would also appreciate it if the approximation formula didn't include the factorial, gamma function, nor any recursive functions. $$f(x)=\prod_{n=1}^{x}\frac{x}{n}$$ Here some examples of the equations outputted. $$(1/1) = 1$$ $$(2/2)*(2/1) = 2$$ $$(3/3)*(3/2)*(3/1) = 4.5$$ $$(4/4)*(4/3)*(4/2)*(4/1) = 10.66...$$ $$(5/5)*(5/4)*(5/3)*(5/2)*(5/1) = 26.0416...$$ $$(6/6)*(6/5)*(6/4)*(6/3)*(6/2)*(6/1) = 64.8$$
2026-04-01 04:51:55.1775019115
Multiplicative Harmonic Series
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