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In this paper the operator $A = u(z)\frac{d}{dz}$ is considered, where $u$ isan arbitrary entire function. The expansion of $A^{k}$ ($k\geq1$) with the helpof powers of differential operators is obtained, and it is shown that thisexpansion depends on special numbers. A connection between these numbers andknown combinatorial numbers is given.

Powers of the operator $u(z)\frac{d}{dz}$ and their connection with the combinatorial numbers