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Sun","submitted_at":"2016-11-04T12:58:21Z","abstract_excerpt":"In this paper, we consider two particular binomial sums \\begin{align*} \\sum_{k=0}^{n-1}(20k^2+8k+1){\\binom{2k}{k}}^5 (-4096)^{n-k-1} \\end{align*} and \\begin{align*} \\sum_{k=0}^{n-1}(120k^2+34k+3){\\binom{2k}{k}}^4\\binom{4k}{2k} 65536^{n-k-1}, \\end{align*} which are inspired by two series for $\\frac{1}{\\pi^2}$ obtained by Guillera. We consider their divisibility properties and prove that they are divisible by $2n^2 \\binom{2n}{n}^2$ for all integer $n\\geq 2$. 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