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The $n$-th Catalan number $c_n$ has the closed form $\frac1{n+1}\binom{2n}{n}$ and follows the recursion $c_n = \sum\limits_{i = 0}^{n-1} c_{n-1-i}c_i$

I am interested in the quantity $e_n$ which follows the recursion $e_n= (n-1) \sum\limits_{i = 1}^{n-1}{e_i e_{n-i}}$ for $n > 1$, with $e_1 = 1$.

I am wondering if it is possible to approximate $e_n$ using $c_n$?

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    btw: it is known that $lim_{n\to\infty} e_n / (2n-1)!! = 1/e$2012-05-09

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