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If $r \\leq c \\frac{n}{\\ln n}$ then all bounds have a type $A_1(n, \\ln n, r)(\\frac{r}{r-1})^n \\leq p(n, r) \\leq A_2(n, r, \\ln r) (\\frac{r}{r-1})^n$, where $A_1$, $A_2$ are some algebraic fractions. 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