What is the asymptotic value of
$$\max\ \frac{(a+b)!(c+d)!b}{a!b!c!d!(b+d)}, \quad \textrm{if}\ \ a+b+c+d=n?$$
Is it $\approx 2^n/n$? Is it related to the asymptotic value of the Catalan numbers?
2026-03-28 16:58:07.1774717087
What is the asymptotic value of MAX $(a+b)!(c+d)!b/(a!b!c!d!(b+d))$ if $a+b+c+d=n$?
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