Anderson-Thakur polynomials and multizeta values in positive characteristic

Multizeta values in positive characteristic were first introduced and studied by Thakur. He and Lara Rodr'{\i}guez discovered and conjectured certain zeta-like families. Kuan and Lin stated more conjectures about zeta-like multizeta values. In the present paper we study and give a transparent formula for certain Anderson-Thakur polynomials. Besides, we confirm the conjectured zeta-like families.