In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics. Keywords Sum • Identity • Beta function • Polygamma function • Gauss hypergeometric function • Determinant • Binomial inversion formula • Derivative formula for a ratio of two differential functions

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