Stieltjes moment sequences and continued fractions play an important role in different mathematical branches. Many famous combinatorial triangles satisfy certain recurrence relations. In this talk, we will present some relations among different combinatorial triangles or combinatorial countings. Then we will give continued fraction expansions from different combinatorial triangles or combinatorial countings. Using continued fraction expansions, we get Hankel-total-positivity and Stieltjes moment properties of combinatorial sequences.