Multifold Convolutions, Generating Functions and 1d Random Walks

Timothy Li, Shannon Starr

We consider multifold convolutions of a combinatorial sequence $(a_n{)}_{n=0}^{\infty }$: namely, for each $k\in \mathbb{N}$ the $k$-fold convolution is $\mathcal{M}^{(k)}_n(\boldsymbol{a})…