Abstract
We give a generalization of the identity proved by J. Worpitzky in [4], by expressing each power x n as a linear combination of the images of β m under the powers of the shift operator E (here $\beta_m(x):=\frac{x^{\underline{m}}}{m!}$ ). We encode the coefficients of these linear combinations in a 3-dimensional array - the Eulerian octant - and we find recurrences formulae, explicit expressions and generating functions for its entries. Keywords: Recursive matrices, Eulerian numbers Mathematics Subject Classification (2000): 05A19
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