In this paper, we confirm several conjectures of Sun on Hankel-type determinants for some combinatorial sequences including Franel numbers, Domb numbers and Apéry numbers. For any nonnegative integer [Formula: see text], define [Formula: see text] [Formula: see text] For [Formula: see text], we show that [Formula: see text] and [Formula: see text] are positive odd integers, and [Formula: see text] and [Formula: see text] are always integers.