I would like to know if the following recurrence relation for Catalan numbers (see mathoverflow.net/questions/191524 and also math.stackexchange.com/questions/2113830) has appeared in a paper or a book, so that I can cite it.
$$C_n = 1 + \sum_{k=1}^{\left\lceil\frac{n}{2} \right\rceil
} (-1)^{k+...
In the classical problem of bracketing $n$ numbers, I know the response is $C_{n-1}$. I find this
$$C_{n-1}=\sum_{i=1}^{\left\lfloor\frac{n}{2}\right\rfloor}(-1)^{i+1}\binom{n-i}{i}C_{n-1-i}$$
but I can't prove that.
Can someone help me?
Regards.
In the classical problem of bracketing $n$ numbers, I know the response is $C_{n-1}$. I find this
$$C_{n-1}=\sum_{i=1}^{\left\lfloor\frac{n}{2}\right\rfloor}(-1)^{i+1}\binom{n-i}{i}C_{n-1-i}$$
but I can't prove that.
Can someone help me?
Regards.
