Rec ently, Sun defined a newsequence $a(n)= sum_{k=0}^n {nchoose 2k}{2kchoose k}rac{1}{2k-1} $, which can be viewed as an analogue of Motzkin numbers. Sun conjectured that the sequence ${rac{a(n+1)}{a(n)}}_{ngeq 5} $ is strictly increasing with limit 3, and the sequence ${ sqrt[n+1]{a(n+1)}/sqrt[n]{a(n)}}_{ngeq 9} $ is strictly decreasing with limit 1. In this paper, we confirm Sun's conjecture.
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