Reccurent convolution evaluation in R

Question

I want to compute the convolution of order 3 which is defined as follows:

so firstly i compute the convolution of order 2. This I can do it properly. My problem is how I can keep the convolution of order 2 (which actually is an integral) as a function in order to use it for the computation of convolution of order 3. Actually I want to do this recurrently in order to compute the convolution of order n.

Thank you in advance