Hi

I am learning FFT. ChatGPT told me that FFT could assist in solving self-convolution form like Catalan number where the (n+1)-th element is some convolution of the first n elements. For example:

c[n + 1] = sum(c[i][n — i]) for i in 0..n

Unfortunately, no matter where I look (and how hard I press ChatGPT), I couldn't find a single website/book/paper detailing this approach.

My Question: Is it actually possible to compute the first n elements of a self-convolution form like Catalan using FFT in, for example, O(nlogn) or less than O(n^2)?

Thanks a lot