Recently, the study of patterns in inversion sequences was initiated by Corteel–Martinez–Savage–Weselcouch and Mansour–Shattuck independently. Motivated their works a double Eulerian equidistribution due to Foata (1977), we investigate several classical statistics on restricted that are either known or conjectured be enumerated Catalan, Large Schröder, Baxter Euler numbers. One two highlights o...