Hankel Determinants for Some Common Lattice Paths

Robert A. Sulanke, Guoce Xin

For a single value of $\ell$, let $f(n,\ell )$ denote the number of lattice paths that use the steps $(1,1)$, $(1,-1)$, and $(\ell ,0)$, that run from $(0,0)$ to $(n,0)$, and that ne…