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We give some formulas of poly-Cauchy numbers by the $r$-Stirling transform.In the case of the classical or poly-Bernoulli numbers, the formulas are withStirling numbers of the first kind. In our case of the classical or poly-Cauchynumbers, the formulas are with Stirling numbers of the second kind. We alsodiscuss annihilation formulas for poly-Cauchy number with negative indices.

Recurrence relations of poly-Cauchy numbers by the $r$-Stirling transform